Use DeMoivre's Theorem to simplify

Question

 

[2(cos40°+isin40°)]5

Answer 1

32(cos200 + isin200)

= about 32(-0.934+i(-0.342))

= -29.89-10.94i

general formula is

(cosA + isinA)^n = cos(nA) + isin(nA)

(cos40+isin40)^5 = cos200+ isin200

2^5 = 32