Hello, i need help to calcul:

Question

( 1/2 ( -1 + i^3 )) ^2
Thanks for your help.

Answer 1

(1/2) (-1+i^3)^2
= (1/2) (1 - 2i^3 + i^6)

now:
i^2 = -1
i^3 = i i^2 = -i
i^6 = (i^3)^2 = i^2 = -1

so back...
= (1/2) (1 - 2(-i) + (-1) )
= (1/2) (2i)
= i