y^77=3 (уравнение)

Найду корень уравнения: y^77=3

Вы ввели

 77    
y   = 3

$$y^{77} = 3$$

Подробное решение

Дано уравнение
$$y^{77} = 3$$
Т.к. степень в ур-нии равна = 77 - не содержит чётного числа в числителе, то
ур-ние будет иметь один действительный корень.
Извлечём корень 77-й степени из обеих частей ур-ния:
Получим:
$$\sqrt[77]{y^{77}} = \sqrt[77]{3}$$
или
$$y = \sqrt[77]{3}$$
Раскрываем скобочки в правой части ур-ния

y = 3^1/77

Получим ответ: y = 3^(1/77)

Остальные 76 корня(ей) являются комплексными.
сделаем замену:
$$z = y$$
тогда ур-ние будет таким:
$$z^{77} = 3$$
Любое комплексное число можно представить так:
$$z = r e^{i p}$$
подставляем в уравнение
$$r^{77} e^{77 i p} = 3$$
где
$$r = \sqrt[77]{3}$$
- модуль комплексного числа
Подставляем r:
$$e^{77 i p} = 1$$
Используя формулу Эйлера, найдём корни для p
$$i \sin{\left (77 p \right )} + \cos{\left (77 p \right )} = 1$$
значит
$$\cos{\left (77 p \right )} = 1$$
и
$$\sin{\left (77 p \right )} = 0$$
тогда
$$p = \frac{2 \pi}{77} N$$
где N=0,1,2,3,...
Перебирая значения N и подставив p в формулу для z
Значит, решением будет для z:
$$z_{1} = \sqrt[77]{3}$$
$$z_{2} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{\pi}{77} \right )}$$
$$z_{3} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{\pi}{77} \right )}$$
$$z_{4} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{77} \right )}$$
$$z_{5} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{77} \right )}$$
$$z_{6} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{77} \right )}$$
$$z_{7} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{77} \right )}$$
$$z_{8} = \sqrt[77]{3} \cos{\left (\frac{4 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{4 \pi}{77} \right )}$$
$$z_{9} = \sqrt[77]{3} \cos{\left (\frac{4 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{4 \pi}{77} \right )}$$
$$z_{10} = - \sqrt[77]{3} \cos{\left (\frac{5 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{5 \pi}{77} \right )}$$
$$z_{11} = - \sqrt[77]{3} \cos{\left (\frac{5 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{5 \pi}{77} \right )}$$
$$z_{12} = \sqrt[77]{3} \cos{\left (\frac{6 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{6 \pi}{77} \right )}$$
$$z_{13} = \sqrt[77]{3} \cos{\left (\frac{6 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{6 \pi}{77} \right )}$$
$$z_{14} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{\pi}{11} \right )}$$
$$z_{15} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{\pi}{11} \right )}$$
$$z_{16} = \sqrt[77]{3} \cos{\left (\frac{8 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{8 \pi}{77} \right )}$$
$$z_{17} = \sqrt[77]{3} \cos{\left (\frac{8 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{8 \pi}{77} \right )}$$
$$z_{18} = - \sqrt[77]{3} \cos{\left (\frac{9 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{9 \pi}{77} \right )}$$
$$z_{19} = - \sqrt[77]{3} \cos{\left (\frac{9 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{9 \pi}{77} \right )}$$
$$z_{20} = \sqrt[77]{3} \cos{\left (\frac{10 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{10 \pi}{77} \right )}$$
$$z_{21} = \sqrt[77]{3} \cos{\left (\frac{10 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{10 \pi}{77} \right )}$$
$$z_{22} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{7} \right )} - \sqrt[77]{3} i \sin{\left (\frac{\pi}{7} \right )}$$
$$z_{23} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{7} \right )} + \sqrt[77]{3} i \sin{\left (\frac{\pi}{7} \right )}$$
$$z_{24} = \sqrt[77]{3} \cos{\left (\frac{12 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{12 \pi}{77} \right )}$$
$$z_{25} = \sqrt[77]{3} \cos{\left (\frac{12 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{12 \pi}{77} \right )}$$
$$z_{26} = - \sqrt[77]{3} \cos{\left (\frac{13 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{13 \pi}{77} \right )}$$
$$z_{27} = - \sqrt[77]{3} \cos{\left (\frac{13 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{13 \pi}{77} \right )}$$
$$z_{28} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{11} \right )}$$
$$z_{29} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{11} \right )}$$
$$z_{30} = - \sqrt[77]{3} \cos{\left (\frac{15 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{15 \pi}{77} \right )}$$
$$z_{31} = - \sqrt[77]{3} \cos{\left (\frac{15 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{15 \pi}{77} \right )}$$
$$z_{32} = \sqrt[77]{3} \cos{\left (\frac{16 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{16 \pi}{77} \right )}$$
$$z_{33} = \sqrt[77]{3} \cos{\left (\frac{16 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{16 \pi}{77} \right )}$$
$$z_{34} = - \sqrt[77]{3} \cos{\left (\frac{17 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{17 \pi}{77} \right )}$$
$$z_{35} = - \sqrt[77]{3} \cos{\left (\frac{17 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{17 \pi}{77} \right )}$$
$$z_{36} = \sqrt[77]{3} \cos{\left (\frac{18 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{18 \pi}{77} \right )}$$
$$z_{37} = \sqrt[77]{3} \cos{\left (\frac{18 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{18 \pi}{77} \right )}$$
$$z_{38} = - \sqrt[77]{3} \cos{\left (\frac{19 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{19 \pi}{77} \right )}$$
$$z_{39} = - \sqrt[77]{3} \cos{\left (\frac{19 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{19 \pi}{77} \right )}$$
$$z_{40} = \sqrt[77]{3} \cos{\left (\frac{20 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{20 \pi}{77} \right )}$$
$$z_{41} = \sqrt[77]{3} \cos{\left (\frac{20 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{20 \pi}{77} \right )}$$
$$z_{42} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{11} \right )}$$
$$z_{43} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{11} \right )}$$
$$z_{44} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{7} \right )} - \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{7} \right )}$$
$$z_{45} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{7} \right )} + \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{7} \right )}$$
$$z_{46} = - \sqrt[77]{3} \cos{\left (\frac{23 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{23 \pi}{77} \right )}$$
$$z_{47} = - \sqrt[77]{3} \cos{\left (\frac{23 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{23 \pi}{77} \right )}$$
$$z_{48} = \sqrt[77]{3} \cos{\left (\frac{24 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{24 \pi}{77} \right )}$$
$$z_{49} = \sqrt[77]{3} \cos{\left (\frac{24 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{24 \pi}{77} \right )}$$
$$z_{50} = - \sqrt[77]{3} \cos{\left (\frac{25 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{25 \pi}{77} \right )}$$
$$z_{51} = - \sqrt[77]{3} \cos{\left (\frac{25 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{25 \pi}{77} \right )}$$
$$z_{52} = \sqrt[77]{3} \cos{\left (\frac{26 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{26 \pi}{77} \right )}$$
$$z_{53} = \sqrt[77]{3} \cos{\left (\frac{26 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{26 \pi}{77} \right )}$$
$$z_{54} = - \sqrt[77]{3} \cos{\left (\frac{27 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{27 \pi}{77} \right )}$$
$$z_{55} = - \sqrt[77]{3} \cos{\left (\frac{27 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{27 \pi}{77} \right )}$$
$$z_{56} = \sqrt[77]{3} \cos{\left (\frac{4 \pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{4 \pi}{11} \right )}$$
$$z_{57} = \sqrt[77]{3} \cos{\left (\frac{4 \pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{4 \pi}{11} \right )}$$
$$z_{58} = - \sqrt[77]{3} \cos{\left (\frac{29 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{29 \pi}{77} \right )}$$
$$z_{59} = - \sqrt[77]{3} \cos{\left (\frac{29 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{29 \pi}{77} \right )}$$
$$z_{60} = \sqrt[77]{3} \cos{\left (\frac{30 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{30 \pi}{77} \right )}$$
$$z_{61} = \sqrt[77]{3} \cos{\left (\frac{30 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{30 \pi}{77} \right )}$$
$$z_{62} = - \sqrt[77]{3} \cos{\left (\frac{31 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{31 \pi}{77} \right )}$$
$$z_{63} = - \sqrt[77]{3} \cos{\left (\frac{31 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{31 \pi}{77} \right )}$$
$$z_{64} = \sqrt[77]{3} \cos{\left (\frac{32 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{32 \pi}{77} \right )}$$
$$z_{65} = \sqrt[77]{3} \cos{\left (\frac{32 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{32 \pi}{77} \right )}$$
$$z_{66} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{7} \right )} - \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{7} \right )}$$
$$z_{67} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{7} \right )} + \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{7} \right )}$$
$$z_{68} = \sqrt[77]{3} \cos{\left (\frac{34 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{34 \pi}{77} \right )}$$
$$z_{69} = \sqrt[77]{3} \cos{\left (\frac{34 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{34 \pi}{77} \right )}$$
$$z_{70} = - \sqrt[77]{3} \cos{\left (\frac{5 \pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{5 \pi}{11} \right )}$$
$$z_{71} = - \sqrt[77]{3} \cos{\left (\frac{5 \pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{5 \pi}{11} \right )}$$
$$z_{72} = \sqrt[77]{3} \cos{\left (\frac{36 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{36 \pi}{77} \right )}$$
$$z_{73} = \sqrt[77]{3} \cos{\left (\frac{36 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{36 \pi}{77} \right )}$$
$$z_{74} = - \sqrt[77]{3} \cos{\left (\frac{37 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{37 \pi}{77} \right )}$$
$$z_{75} = - \sqrt[77]{3} \cos{\left (\frac{37 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{37 \pi}{77} \right )}$$
$$z_{76} = \sqrt[77]{3} \cos{\left (\frac{38 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{38 \pi}{77} \right )}$$
$$z_{77} = \sqrt[77]{3} \cos{\left (\frac{38 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{38 \pi}{77} \right )}$$
делаем обратную замену
$$z = y$$
$$y = z$$

Тогда, окончательный ответ:
$$y_{1} = \sqrt[77]{3}$$
$$y_{2} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{\pi}{77} \right )}$$
$$y_{3} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{\pi}{77} \right )}$$
$$y_{4} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{77} \right )}$$
$$y_{5} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{77} \right )}$$
$$y_{6} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{77} \right )}$$
$$y_{7} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{77} \right )}$$
$$y_{8} = \sqrt[77]{3} \cos{\left (\frac{4 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{4 \pi}{77} \right )}$$
$$y_{9} = \sqrt[77]{3} \cos{\left (\frac{4 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{4 \pi}{77} \right )}$$
$$y_{10} = - \sqrt[77]{3} \cos{\left (\frac{5 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{5 \pi}{77} \right )}$$
$$y_{11} = - \sqrt[77]{3} \cos{\left (\frac{5 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{5 \pi}{77} \right )}$$
$$y_{12} = \sqrt[77]{3} \cos{\left (\frac{6 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{6 \pi}{77} \right )}$$
$$y_{13} = \sqrt[77]{3} \cos{\left (\frac{6 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{6 \pi}{77} \right )}$$
$$y_{14} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{\pi}{11} \right )}$$
$$y_{15} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{\pi}{11} \right )}$$
$$y_{16} = \sqrt[77]{3} \cos{\left (\frac{8 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{8 \pi}{77} \right )}$$
$$y_{17} = \sqrt[77]{3} \cos{\left (\frac{8 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{8 \pi}{77} \right )}$$
$$y_{18} = - \sqrt[77]{3} \cos{\left (\frac{9 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{9 \pi}{77} \right )}$$
$$y_{19} = - \sqrt[77]{3} \cos{\left (\frac{9 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{9 \pi}{77} \right )}$$
$$y_{20} = \sqrt[77]{3} \cos{\left (\frac{10 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{10 \pi}{77} \right )}$$
$$y_{21} = \sqrt[77]{3} \cos{\left (\frac{10 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{10 \pi}{77} \right )}$$
$$y_{22} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{7} \right )} - \sqrt[77]{3} i \sin{\left (\frac{\pi}{7} \right )}$$
$$y_{23} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{7} \right )} + \sqrt[77]{3} i \sin{\left (\frac{\pi}{7} \right )}$$
$$y_{24} = \sqrt[77]{3} \cos{\left (\frac{12 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{12 \pi}{77} \right )}$$
$$y_{25} = \sqrt[77]{3} \cos{\left (\frac{12 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{12 \pi}{77} \right )}$$
$$y_{26} = - \sqrt[77]{3} \cos{\left (\frac{13 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{13 \pi}{77} \right )}$$
$$y_{27} = - \sqrt[77]{3} \cos{\left (\frac{13 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{13 \pi}{77} \right )}$$
$$y_{28} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{11} \right )}$$
$$y_{29} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{11} \right )}$$
$$y_{30} = - \sqrt[77]{3} \cos{\left (\frac{15 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{15 \pi}{77} \right )}$$
$$y_{31} = - \sqrt[77]{3} \cos{\left (\frac{15 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{15 \pi}{77} \right )}$$
$$y_{32} = \sqrt[77]{3} \cos{\left (\frac{16 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{16 \pi}{77} \right )}$$
$$y_{33} = \sqrt[77]{3} \cos{\left (\frac{16 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{16 \pi}{77} \right )}$$
$$y_{34} = - \sqrt[77]{3} \cos{\left (\frac{17 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{17 \pi}{77} \right )}$$
$$y_{35} = - \sqrt[77]{3} \cos{\left (\frac{17 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{17 \pi}{77} \right )}$$
$$y_{36} = \sqrt[77]{3} \cos{\left (\frac{18 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{18 \pi}{77} \right )}$$
$$y_{37} = \sqrt[77]{3} \cos{\left (\frac{18 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{18 \pi}{77} \right )}$$
$$y_{38} = - \sqrt[77]{3} \cos{\left (\frac{19 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{19 \pi}{77} \right )}$$
$$y_{39} = - \sqrt[77]{3} \cos{\left (\frac{19 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{19 \pi}{77} \right )}$$
$$y_{40} = \sqrt[77]{3} \cos{\left (\frac{20 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{20 \pi}{77} \right )}$$
$$y_{41} = \sqrt[77]{3} \cos{\left (\frac{20 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{20 \pi}{77} \right )}$$
$$y_{42} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{11} \right )}$$
$$y_{43} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{11} \right )}$$
$$y_{44} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{7} \right )} - \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{7} \right )}$$
$$y_{45} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{7} \right )} + \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{7} \right )}$$
$$y_{46} = - \sqrt[77]{3} \cos{\left (\frac{23 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{23 \pi}{77} \right )}$$
$$y_{47} = - \sqrt[77]{3} \cos{\left (\frac{23 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{23 \pi}{77} \right )}$$
$$y_{48} = \sqrt[77]{3} \cos{\left (\frac{24 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{24 \pi}{77} \right )}$$
$$y_{49} = \sqrt[77]{3} \cos{\left (\frac{24 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{24 \pi}{77} \right )}$$
$$y_{50} = - \sqrt[77]{3} \cos{\left (\frac{25 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{25 \pi}{77} \right )}$$
$$y_{51} = - \sqrt[77]{3} \cos{\left (\frac{25 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{25 \pi}{77} \right )}$$
$$y_{52} = \sqrt[77]{3} \cos{\left (\frac{26 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{26 \pi}{77} \right )}$$
$$y_{53} = \sqrt[77]{3} \cos{\left (\frac{26 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{26 \pi}{77} \right )}$$
$$y_{54} = - \sqrt[77]{3} \cos{\left (\frac{27 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{27 \pi}{77} \right )}$$
$$y_{55} = - \sqrt[77]{3} \cos{\left (\frac{27 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{27 \pi}{77} \right )}$$
$$y_{56} = \sqrt[77]{3} \cos{\left (\frac{4 \pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{4 \pi}{11} \right )}$$
$$y_{57} = \sqrt[77]{3} \cos{\left (\frac{4 \pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{4 \pi}{11} \right )}$$
$$y_{58} = - \sqrt[77]{3} \cos{\left (\frac{29 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{29 \pi}{77} \right )}$$
$$y_{59} = - \sqrt[77]{3} \cos{\left (\frac{29 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{29 \pi}{77} \right )}$$
$$y_{60} = \sqrt[77]{3} \cos{\left (\frac{30 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{30 \pi}{77} \right )}$$
$$y_{61} = \sqrt[77]{3} \cos{\left (\frac{30 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{30 \pi}{77} \right )}$$
$$y_{62} = - \sqrt[77]{3} \cos{\left (\frac{31 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{31 \pi}{77} \right )}$$
$$y_{63} = - \sqrt[77]{3} \cos{\left (\frac{31 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{31 \pi}{77} \right )}$$
$$y_{64} = \sqrt[77]{3} \cos{\left (\frac{32 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{32 \pi}{77} \right )}$$
$$y_{65} = \sqrt[77]{3} \cos{\left (\frac{32 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{32 \pi}{77} \right )}$$
$$y_{66} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{7} \right )} - \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{7} \right )}$$
$$y_{67} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{7} \right )} + \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{7} \right )}$$
$$y_{68} = \sqrt[77]{3} \cos{\left (\frac{34 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{34 \pi}{77} \right )}$$
$$y_{69} = \sqrt[77]{3} \cos{\left (\frac{34 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{34 \pi}{77} \right )}$$
$$y_{70} = - \sqrt[77]{3} \cos{\left (\frac{5 \pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{5 \pi}{11} \right )}$$
$$y_{71} = - \sqrt[77]{3} \cos{\left (\frac{5 \pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{5 \pi}{11} \right )}$$
$$y_{72} = \sqrt[77]{3} \cos{\left (\frac{36 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{36 \pi}{77} \right )}$$
$$y_{73} = \sqrt[77]{3} \cos{\left (\frac{36 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{36 \pi}{77} \right )}$$
$$y_{74} = - \sqrt[77]{3} \cos{\left (\frac{37 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{37 \pi}{77} \right )}$$
$$y_{75} = - \sqrt[77]{3} \cos{\left (\frac{37 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{37 \pi}{77} \right )}$$
$$y_{76} = \sqrt[77]{3} \cos{\left (\frac{38 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{38 \pi}{77} \right )}$$
$$y_{77} = \sqrt[77]{3} \cos{\left (\frac{38 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{38 \pi}{77} \right )}$$

Быстрый ответ

     77___
y1 = \/ 3 

$$y_{1} = \sqrt[77]{3}$$

       77___    /pi\     77___    /pi\
y2 = - \/ 3 *cos|--| - I*\/ 3 *sin|--|
                \77/              \77/

$$y_{2} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{\pi}{77} \right )}$$

       77___    /pi\     77___    /pi\
y3 = - \/ 3 *cos|--| + I*\/ 3 *sin|--|
                \77/              \77/

$$y_{3} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{\pi}{77} \right )}$$

     77___    /2*pi\     77___    /2*pi\
y4 = \/ 3 *cos|----| - I*\/ 3 *sin|----|
              \ 77 /              \ 77 /

$$y_{4} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{77} \right )}$$

     77___    /2*pi\     77___    /2*pi\
y5 = \/ 3 *cos|----| + I*\/ 3 *sin|----|
              \ 77 /              \ 77 /

$$y_{5} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{77} \right )}$$

       77___    /3*pi\     77___    /3*pi\
y6 = - \/ 3 *cos|----| - I*\/ 3 *sin|----|
                \ 77 /              \ 77 /

$$y_{6} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{77} \right )}$$

       77___    /3*pi\     77___    /3*pi\
y7 = - \/ 3 *cos|----| + I*\/ 3 *sin|----|
                \ 77 /              \ 77 /

$$y_{7} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{77} \right )}$$

     77___    /4*pi\     77___    /4*pi\
y8 = \/ 3 *cos|----| - I*\/ 3 *sin|----|
              \ 77 /              \ 77 /

$$y_{8} = \sqrt[77]{3} \cos{\left (\frac{4 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{4 \pi}{77} \right )}$$

     77___    /4*pi\     77___    /4*pi\
y9 = \/ 3 *cos|----| + I*\/ 3 *sin|----|
              \ 77 /              \ 77 /

$$y_{9} = \sqrt[77]{3} \cos{\left (\frac{4 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{4 \pi}{77} \right )}$$

        77___    /5*pi\     77___    /5*pi\
y10 = - \/ 3 *cos|----| - I*\/ 3 *sin|----|
                 \ 77 /              \ 77 /

$$y_{10} = - \sqrt[77]{3} \cos{\left (\frac{5 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{5 \pi}{77} \right )}$$

        77___    /5*pi\     77___    /5*pi\
y11 = - \/ 3 *cos|----| + I*\/ 3 *sin|----|
                 \ 77 /              \ 77 /

$$y_{11} = - \sqrt[77]{3} \cos{\left (\frac{5 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{5 \pi}{77} \right )}$$

      77___    /6*pi\     77___    /6*pi\
y12 = \/ 3 *cos|----| - I*\/ 3 *sin|----|
               \ 77 /              \ 77 /

$$y_{12} = \sqrt[77]{3} \cos{\left (\frac{6 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{6 \pi}{77} \right )}$$

      77___    /6*pi\     77___    /6*pi\
y13 = \/ 3 *cos|----| + I*\/ 3 *sin|----|
               \ 77 /              \ 77 /

$$y_{13} = \sqrt[77]{3} \cos{\left (\frac{6 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{6 \pi}{77} \right )}$$

        77___    /pi\     77___    /pi\
y14 = - \/ 3 *cos|--| - I*\/ 3 *sin|--|
                 \11/              \11/

$$y_{14} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{\pi}{11} \right )}$$

        77___    /pi\     77___    /pi\
y15 = - \/ 3 *cos|--| + I*\/ 3 *sin|--|
                 \11/              \11/

$$y_{15} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{\pi}{11} \right )}$$

      77___    /8*pi\     77___    /8*pi\
y16 = \/ 3 *cos|----| - I*\/ 3 *sin|----|
               \ 77 /              \ 77 /

$$y_{16} = \sqrt[77]{3} \cos{\left (\frac{8 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{8 \pi}{77} \right )}$$

      77___    /8*pi\     77___    /8*pi\
y17 = \/ 3 *cos|----| + I*\/ 3 *sin|----|
               \ 77 /              \ 77 /

$$y_{17} = \sqrt[77]{3} \cos{\left (\frac{8 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{8 \pi}{77} \right )}$$

        77___    /9*pi\     77___    /9*pi\
y18 = - \/ 3 *cos|----| - I*\/ 3 *sin|----|
                 \ 77 /              \ 77 /

$$y_{18} = - \sqrt[77]{3} \cos{\left (\frac{9 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{9 \pi}{77} \right )}$$

        77___    /9*pi\     77___    /9*pi\
y19 = - \/ 3 *cos|----| + I*\/ 3 *sin|----|
                 \ 77 /              \ 77 /

$$y_{19} = - \sqrt[77]{3} \cos{\left (\frac{9 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{9 \pi}{77} \right )}$$

      77___    /10*pi\     77___    /10*pi\
y20 = \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{20} = \sqrt[77]{3} \cos{\left (\frac{10 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{10 \pi}{77} \right )}$$

      77___    /10*pi\     77___    /10*pi\
y21 = \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{21} = \sqrt[77]{3} \cos{\left (\frac{10 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{10 \pi}{77} \right )}$$

        77___    /pi\     77___    /pi\
y22 = - \/ 3 *cos|--| - I*\/ 3 *sin|--|
                 \7 /              \7 /

$$y_{22} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{7} \right )} - \sqrt[77]{3} i \sin{\left (\frac{\pi}{7} \right )}$$

        77___    /pi\     77___    /pi\
y23 = - \/ 3 *cos|--| + I*\/ 3 *sin|--|
                 \7 /              \7 /

$$y_{23} = - \sqrt[77]{3} \cos{\left (\frac{\pi}{7} \right )} + \sqrt[77]{3} i \sin{\left (\frac{\pi}{7} \right )}$$

      77___    /12*pi\     77___    /12*pi\
y24 = \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{24} = \sqrt[77]{3} \cos{\left (\frac{12 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{12 \pi}{77} \right )}$$

      77___    /12*pi\     77___    /12*pi\
y25 = \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{25} = \sqrt[77]{3} \cos{\left (\frac{12 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{12 \pi}{77} \right )}$$

        77___    /13*pi\     77___    /13*pi\
y26 = - \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{26} = - \sqrt[77]{3} \cos{\left (\frac{13 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{13 \pi}{77} \right )}$$

        77___    /13*pi\     77___    /13*pi\
y27 = - \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{27} = - \sqrt[77]{3} \cos{\left (\frac{13 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{13 \pi}{77} \right )}$$

      77___    /2*pi\     77___    /2*pi\
y28 = \/ 3 *cos|----| - I*\/ 3 *sin|----|
               \ 11 /              \ 11 /

$$y_{28} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{11} \right )}$$

      77___    /2*pi\     77___    /2*pi\
y29 = \/ 3 *cos|----| + I*\/ 3 *sin|----|
               \ 11 /              \ 11 /

$$y_{29} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{11} \right )}$$

        77___    /15*pi\     77___    /15*pi\
y30 = - \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{30} = - \sqrt[77]{3} \cos{\left (\frac{15 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{15 \pi}{77} \right )}$$

        77___    /15*pi\     77___    /15*pi\
y31 = - \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{31} = - \sqrt[77]{3} \cos{\left (\frac{15 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{15 \pi}{77} \right )}$$

      77___    /16*pi\     77___    /16*pi\
y32 = \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{32} = \sqrt[77]{3} \cos{\left (\frac{16 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{16 \pi}{77} \right )}$$

      77___    /16*pi\     77___    /16*pi\
y33 = \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{33} = \sqrt[77]{3} \cos{\left (\frac{16 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{16 \pi}{77} \right )}$$

        77___    /17*pi\     77___    /17*pi\
y34 = - \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{34} = - \sqrt[77]{3} \cos{\left (\frac{17 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{17 \pi}{77} \right )}$$

        77___    /17*pi\     77___    /17*pi\
y35 = - \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{35} = - \sqrt[77]{3} \cos{\left (\frac{17 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{17 \pi}{77} \right )}$$

      77___    /18*pi\     77___    /18*pi\
y36 = \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{36} = \sqrt[77]{3} \cos{\left (\frac{18 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{18 \pi}{77} \right )}$$

      77___    /18*pi\     77___    /18*pi\
y37 = \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{37} = \sqrt[77]{3} \cos{\left (\frac{18 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{18 \pi}{77} \right )}$$

        77___    /19*pi\     77___    /19*pi\
y38 = - \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{38} = - \sqrt[77]{3} \cos{\left (\frac{19 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{19 \pi}{77} \right )}$$

        77___    /19*pi\     77___    /19*pi\
y39 = - \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{39} = - \sqrt[77]{3} \cos{\left (\frac{19 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{19 \pi}{77} \right )}$$

      77___    /20*pi\     77___    /20*pi\
y40 = \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{40} = \sqrt[77]{3} \cos{\left (\frac{20 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{20 \pi}{77} \right )}$$

      77___    /20*pi\     77___    /20*pi\
y41 = \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{41} = \sqrt[77]{3} \cos{\left (\frac{20 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{20 \pi}{77} \right )}$$

        77___    /3*pi\     77___    /3*pi\
y42 = - \/ 3 *cos|----| - I*\/ 3 *sin|----|
                 \ 11 /              \ 11 /

$$y_{42} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{11} \right )}$$

        77___    /3*pi\     77___    /3*pi\
y43 = - \/ 3 *cos|----| + I*\/ 3 *sin|----|
                 \ 11 /              \ 11 /

$$y_{43} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{11} \right )}$$

      77___    /2*pi\     77___    /2*pi\
y44 = \/ 3 *cos|----| - I*\/ 3 *sin|----|
               \ 7  /              \ 7  /

$$y_{44} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{7} \right )} - \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{7} \right )}$$

      77___    /2*pi\     77___    /2*pi\
y45 = \/ 3 *cos|----| + I*\/ 3 *sin|----|
               \ 7  /              \ 7  /

$$y_{45} = \sqrt[77]{3} \cos{\left (\frac{2 \pi}{7} \right )} + \sqrt[77]{3} i \sin{\left (\frac{2 \pi}{7} \right )}$$

        77___    /23*pi\     77___    /23*pi\
y46 = - \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{46} = - \sqrt[77]{3} \cos{\left (\frac{23 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{23 \pi}{77} \right )}$$

        77___    /23*pi\     77___    /23*pi\
y47 = - \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{47} = - \sqrt[77]{3} \cos{\left (\frac{23 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{23 \pi}{77} \right )}$$

      77___    /24*pi\     77___    /24*pi\
y48 = \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{48} = \sqrt[77]{3} \cos{\left (\frac{24 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{24 \pi}{77} \right )}$$

      77___    /24*pi\     77___    /24*pi\
y49 = \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{49} = \sqrt[77]{3} \cos{\left (\frac{24 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{24 \pi}{77} \right )}$$

        77___    /25*pi\     77___    /25*pi\
y50 = - \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{50} = - \sqrt[77]{3} \cos{\left (\frac{25 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{25 \pi}{77} \right )}$$

        77___    /25*pi\     77___    /25*pi\
y51 = - \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{51} = - \sqrt[77]{3} \cos{\left (\frac{25 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{25 \pi}{77} \right )}$$

      77___    /26*pi\     77___    /26*pi\
y52 = \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{52} = \sqrt[77]{3} \cos{\left (\frac{26 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{26 \pi}{77} \right )}$$

      77___    /26*pi\     77___    /26*pi\
y53 = \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{53} = \sqrt[77]{3} \cos{\left (\frac{26 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{26 \pi}{77} \right )}$$

        77___    /27*pi\     77___    /27*pi\
y54 = - \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{54} = - \sqrt[77]{3} \cos{\left (\frac{27 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{27 \pi}{77} \right )}$$

        77___    /27*pi\     77___    /27*pi\
y55 = - \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{55} = - \sqrt[77]{3} \cos{\left (\frac{27 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{27 \pi}{77} \right )}$$

      77___    /4*pi\     77___    /4*pi\
y56 = \/ 3 *cos|----| - I*\/ 3 *sin|----|
               \ 11 /              \ 11 /

$$y_{56} = \sqrt[77]{3} \cos{\left (\frac{4 \pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{4 \pi}{11} \right )}$$

      77___    /4*pi\     77___    /4*pi\
y57 = \/ 3 *cos|----| + I*\/ 3 *sin|----|
               \ 11 /              \ 11 /

$$y_{57} = \sqrt[77]{3} \cos{\left (\frac{4 \pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{4 \pi}{11} \right )}$$

        77___    /29*pi\     77___    /29*pi\
y58 = - \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{58} = - \sqrt[77]{3} \cos{\left (\frac{29 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{29 \pi}{77} \right )}$$

        77___    /29*pi\     77___    /29*pi\
y59 = - \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{59} = - \sqrt[77]{3} \cos{\left (\frac{29 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{29 \pi}{77} \right )}$$

      77___    /30*pi\     77___    /30*pi\
y60 = \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{60} = \sqrt[77]{3} \cos{\left (\frac{30 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{30 \pi}{77} \right )}$$

      77___    /30*pi\     77___    /30*pi\
y61 = \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{61} = \sqrt[77]{3} \cos{\left (\frac{30 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{30 \pi}{77} \right )}$$

        77___    /31*pi\     77___    /31*pi\
y62 = - \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{62} = - \sqrt[77]{3} \cos{\left (\frac{31 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{31 \pi}{77} \right )}$$

        77___    /31*pi\     77___    /31*pi\
y63 = - \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{63} = - \sqrt[77]{3} \cos{\left (\frac{31 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{31 \pi}{77} \right )}$$

      77___    /32*pi\     77___    /32*pi\
y64 = \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{64} = \sqrt[77]{3} \cos{\left (\frac{32 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{32 \pi}{77} \right )}$$

      77___    /32*pi\     77___    /32*pi\
y65 = \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{65} = \sqrt[77]{3} \cos{\left (\frac{32 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{32 \pi}{77} \right )}$$

        77___    /3*pi\     77___    /3*pi\
y66 = - \/ 3 *cos|----| - I*\/ 3 *sin|----|
                 \ 7  /              \ 7  /

$$y_{66} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{7} \right )} - \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{7} \right )}$$

        77___    /3*pi\     77___    /3*pi\
y67 = - \/ 3 *cos|----| + I*\/ 3 *sin|----|
                 \ 7  /              \ 7  /

$$y_{67} = - \sqrt[77]{3} \cos{\left (\frac{3 \pi}{7} \right )} + \sqrt[77]{3} i \sin{\left (\frac{3 \pi}{7} \right )}$$

      77___    /34*pi\     77___    /34*pi\
y68 = \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{68} = \sqrt[77]{3} \cos{\left (\frac{34 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{34 \pi}{77} \right )}$$

      77___    /34*pi\     77___    /34*pi\
y69 = \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{69} = \sqrt[77]{3} \cos{\left (\frac{34 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{34 \pi}{77} \right )}$$

        77___    /5*pi\     77___    /5*pi\
y70 = - \/ 3 *cos|----| - I*\/ 3 *sin|----|
                 \ 11 /              \ 11 /

$$y_{70} = - \sqrt[77]{3} \cos{\left (\frac{5 \pi}{11} \right )} - \sqrt[77]{3} i \sin{\left (\frac{5 \pi}{11} \right )}$$

        77___    /5*pi\     77___    /5*pi\
y71 = - \/ 3 *cos|----| + I*\/ 3 *sin|----|
                 \ 11 /              \ 11 /

$$y_{71} = - \sqrt[77]{3} \cos{\left (\frac{5 \pi}{11} \right )} + \sqrt[77]{3} i \sin{\left (\frac{5 \pi}{11} \right )}$$

      77___    /36*pi\     77___    /36*pi\
y72 = \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{72} = \sqrt[77]{3} \cos{\left (\frac{36 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{36 \pi}{77} \right )}$$

      77___    /36*pi\     77___    /36*pi\
y73 = \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{73} = \sqrt[77]{3} \cos{\left (\frac{36 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{36 \pi}{77} \right )}$$

        77___    /37*pi\     77___    /37*pi\
y74 = - \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{74} = - \sqrt[77]{3} \cos{\left (\frac{37 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{37 \pi}{77} \right )}$$

        77___    /37*pi\     77___    /37*pi\
y75 = - \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
                 \  77 /              \  77 /

$$y_{75} = - \sqrt[77]{3} \cos{\left (\frac{37 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{37 \pi}{77} \right )}$$

      77___    /38*pi\     77___    /38*pi\
y76 = \/ 3 *cos|-----| - I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{76} = \sqrt[77]{3} \cos{\left (\frac{38 \pi}{77} \right )} - \sqrt[77]{3} i \sin{\left (\frac{38 \pi}{77} \right )}$$

      77___    /38*pi\     77___    /38*pi\
y77 = \/ 3 *cos|-----| + I*\/ 3 *sin|-----|
               \  77 /              \  77 /

$$y_{77} = \sqrt[77]{3} \cos{\left (\frac{38 \pi}{77} \right )} + \sqrt[77]{3} i \sin{\left (\frac{38 \pi}{77} \right )}$$

Численный ответ

y1 = 0.931107011136 + 0.402475033223*i

y2 = -0.913915755741 + 0.440118631693*i

y3 = 1.01099472902 + 0.082680568804*i

y4 = 0.265868074001 + 0.978907853571*i

y5 = 0.960814280971 + 0.325241965369*i

y6 = -0.973280850592 - 0.285781042803*i

y7 = 0.752899998689 + 0.679770557269*i

y8 = 0.895203377764 - 0.477029696136*i

y9 = -0.599574945577 - 0.818203094098*i

y10 = 0.421384510696 + 0.922703372*i

y11 = -0.830263301045 + 0.582760044524*i

y12 = 1.00089149353 + 0.164810912064*i

y13 = -1.01352580204 + 0.0413747164681*i

y14 = 0.265868074001 - 0.978907853571*i

y15 = -0.144359897003 + 1.00404513778*i

y16 = 0.495191279277 + 0.885286403083*i

y17 = 0.632449326234 + 0.793066370679*i

y18 = 0.185193342114 - 0.997321334672*i

y19 = -0.875001022112 - 0.513146791726*i

y20 = -0.225718551184 - 0.988937588631*i

y21 = 0.853342313611 - 0.548409805124*i

y22 = 0.565702631595 - 0.841977999215*i

y23 = 0.495191279277 - 0.885286403083*i

y24 = 1.01099472902 - 0.082680568804*i

y25 = 0.103286179091 + 1.00909780684*i

y26 = 0.694987174954 - 0.738877016293*i

y27 = 0.98412749029 - 0.245844465896*i

y28 = -0.993336146902 + 0.205498705137*i

y29 = 0.895203377764 + 0.477029696136*i

y30 = -0.780000314694 - 0.648495125373*i

y31 = -0.383398068332 - 0.939123176029*i

y32 = -0.946748530802 + 0.364161554781*i

y33 = 0.565702631595 + 0.841977999215*i

y34 = 0.185193342114 + 0.997321334672*i

y35 = -0.0620405515259 - 1.01247093219*i

y36 = 0.98412749029 + 0.245844465896*i

y37 = 0.103286179091 - 1.00909780684*i

y38 = -0.0620405515259 + 1.01247093219*i

y39 = 0.344773497721 + 0.953979902212*i

y40 = 0.853342313611 + 0.548409805124*i

y41 = -0.305575085648 + 0.967248822996*i

y42 = -0.664271057403 + 0.766609666553*i

y43 = 0.020691663586 + 1.01415889959*i

y44 = 0.752899998689 - 0.679770557269*i

y45 = 0.931107011136 - 0.402475033223*i

y46 = 0.805802397152 + 0.616140337341*i

y47 = 0.694987174954 + 0.738877016293*i

y48 = 0.421384510696 - 0.922703372*i

y49 = -0.530888761411 + 0.864351515046*i

y50 = 0.344773497721 - 0.953979902212*i

y51 = -0.664271057403 - 0.766609666553*i

y52 = 1.00089149353 - 0.164810912064*i

y53 = -0.780000314694 + 0.648495125373*i

y54 = -0.973280850592 + 0.285781042803*i

y55 = -0.830263301045 - 0.582760044524*i

y56 = -0.724546554939 - 0.709914578158*i

y57 = -0.913915755741 - 0.440118631693*i

y58 = -0.383398068332 + 0.939123176029*i

y59 = 0.805802397152 - 0.616140337341*i

y60 = -1.00678095504 - 0.123848807493*i

y61 = -0.993336146902 - 0.205498705137*i

y62 = -0.305575085648 - 0.967248822996*i

y63 = -1.01352580204 - 0.0413747164681*i

y64 = 0.632449326234 - 0.793066370679*i

y65 = 0.020691663586 - 1.01415889959*i

y66 = 0.960814280971 - 0.325241965369*i

y67 = -1.00678095504 + 0.123848807493*i

y68 = -0.458669600129 - 0.90474781927*i

y69 = -0.144359897003 - 1.00404513778*i

y70 = -0.458669600129 + 0.90474781927*i

y71 = -0.599574945577 + 0.818203094098*i

y72 = -0.946748530802 - 0.364161554781*i

y73 = -0.875001022112 + 0.513146791726*i

y74 = -0.225718551184 + 0.988937588631*i

y75 = -0.724546554939 + 0.709914578158*i

y76 = -0.530888761411 - 0.864351515046*i

y77 = 1.01436996138000

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