Evaluating the required result using De Moivre's theorem

[@raghvendrasingh1289]

z^3 = i
z^3+ i^3 = 0 because i^2 = - 1
(z+i) (z^2 - iz - 1) = 0
z = - i , (i+√3)/2 , ( i - √3)/2

[@cipherunity]

Better approach