Use De Moivre's theorem to simplify the expression. Write the answer in a + bi form.

Question

[2(cos 240° + i sin 240°)]^5

Answer 1

z = 2(cos 240° + i sin 240°) =

2 exp(4/3 pi i)

z^5 = 2^5 exp(20/3 pi i) =

32 exp(2/3 pi i) =

-16 + 16 sqrt(3) i

Answer 2

(2cis240°)^5 = 2^5 cis(5*240°)
= 32 cis1200°
= 32 cis120°
= -16 + 16√3 i