find the cube root of 27i and sketch thesse roots in a complex plane

Question

find the cube root of 27i , and sketch these roots in a complex plane

Answer 1

Use De Moivre's Theorem

||27i|| = 27

θ = π/2

 

z = 3(cos π/6 + i sin π/6)

z = 3(cos π/3 + i sin π/3)

z = 3(cos 2π/3 + i sin 2π/3)