Сумма корней w^3+z=0

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    Решение

    Сумма и произведение корней [src]
    сумма
        3        /  3          2         \       2         
    - re (w) + I*\im (w) - 3*re (w)*im(w)/ + 3*im (w)*re(w)
    i(3(re(w))2im(w)+(im(w))3)(re(w))3+3re(w)(im(w))2i \left(- 3 \left(\operatorname{re}{\left(w\right)}\right)^{2} \operatorname{im}{\left(w\right)} + \left(\operatorname{im}{\left(w\right)}\right)^{3}\right) - \left(\operatorname{re}{\left(w\right)}\right)^{3} + 3 \operatorname{re}{\left(w\right)} \left(\operatorname{im}{\left(w\right)}\right)^{2}
    =
        3        /  3          2         \       2         
    - re (w) + I*\im (w) - 3*re (w)*im(w)/ + 3*im (w)*re(w)
    i(3(re(w))2im(w)+(im(w))3)(re(w))3+3re(w)(im(w))2i \left(- 3 \left(\operatorname{re}{\left(w\right)}\right)^{2} \operatorname{im}{\left(w\right)} + \left(\operatorname{im}{\left(w\right)}\right)^{3}\right) - \left(\operatorname{re}{\left(w\right)}\right)^{3} + 3 \operatorname{re}{\left(w\right)} \left(\operatorname{im}{\left(w\right)}\right)^{2}
    произведение
        3        /  3          2         \       2         
    - re (w) + I*\im (w) - 3*re (w)*im(w)/ + 3*im (w)*re(w)
    i(3(re(w))2im(w)+(im(w))3)(re(w))3+3re(w)(im(w))2i \left(- 3 \left(\operatorname{re}{\left(w\right)}\right)^{2} \operatorname{im}{\left(w\right)} + \left(\operatorname{im}{\left(w\right)}\right)^{3}\right) - \left(\operatorname{re}{\left(w\right)}\right)^{3} + 3 \operatorname{re}{\left(w\right)} \left(\operatorname{im}{\left(w\right)}\right)^{2}
    =
        3          2              /  2          2   \      
    - re (w) + 3*im (w)*re(w) + I*\im (w) - 3*re (w)/*im(w)
    i(3(re(w))2+(im(w))2)im(w)(re(w))3+3re(w)(im(w))2i \left(- 3 \left(\operatorname{re}{\left(w\right)}\right)^{2} + \left(\operatorname{im}{\left(w\right)}\right)^{2}\right) \operatorname{im}{\left(w\right)} - \left(\operatorname{re}{\left(w\right)}\right)^{3} + 3 \operatorname{re}{\left(w\right)} \left(\operatorname{im}{\left(w\right)}\right)^{2}