Hi i need help for calcul with a Moivre's theorem:

Question

( 1/2 ( -1 - i√3 )) ^3
thanks for your help

Answer 1

convert (x,y) to (r,θ)
1/2 ( -1 - i√3 ) = (1,4π/3)

(re^iθ)ⁿ = rⁿe^inθ

(1,4π/3)³ = (1³,4π) = (1,4π)
in (x,y) that's (1,0)