Question

18
(cos+ i sin ) ¹8
6

Answer 1

-1.

Explanation:

1) according to the DeMoivre's theorem:

`1*(cos( \pi)/(6) +isin( \pi)/(6))^(18)=1^(18)(cos(18*( \pi)/(6))+isin(18*( \pi)/(6)))=cos3\pi +isin3\pi =cos\pi +isin\pi ;`

2) if cos(π)=-1 and sin(π)=0, then cosπ+i*sin(π)=-1.