Question

Найти корни уравнения z^3=i

Answer 1

$z=sqrt[3]{i}=sqrt[3]{1cdot (cos frac{pi}{2}+isinfrac{pi}{2})}=cosdfrac{frac{pi}{2}+2pi k}{3}+isindfrac{frac{pi}{2}+2pi k}{3},~ k=0,1,2$