Question

Как решать? Кубический корень -i чему равен?

Answer 1

$-i = 0 - i = cos(-\frac{\pi}{2})+isin(-\frac{\pi}{2}) = e^{i(-\frac{\pi}{2}+2\pi n)}, n \in Z\\\sqrt[3]{-i} = \sqrt[3]{e^{i(-\frac{\pi}{2})}}= e^{i(-\frac{\pi}{6} + \frac{2}{3}\pi n)}, n \in Z = cos( -\frac{\pi}{6} + \frac{2}{3}\pi n) + i sin(-\frac{\pi}{6} + \frac{2}{3}\pi n), n \in Z$