Question

How do you use DeMoivre's Theorem to simplify `(2(cos(pi/2)+isin(pi/2)))^8`?

Answer 1

`(2(cos(pi/2)+isin(pi/2)))^8=256`

Explanation:

According to The de Moivre's formula we have:
`(2(cos(pi/2)+isin(pi/2)))^8=2^8 (cos(8*pi/2)+isin(8*pi/2))`.
The rest is just simplifying:
`2^8 (cos(8*pi/2)+isin(8*pi/2))=256(cos(4pi)+isin(4pi))=256(1+i*0)=256`