Question

Найти корни уравнения z^3=i

Answer 1

$z=\sqrt[3]{i}=\sqrt[3]{1\cdot (\cos \frac{\pi}{2}+i\sin\frac{\pi}{2})}=\cos\dfrac{\frac{\pi}{2}+2\pi k}{3}+i\sin\dfrac{\frac{\pi}{2}+2\pi k}{3},~ k=0,1,2$