Question

How do you use DeMoivre's theorem to simplify `(5e^(15i))^3`?

Answer 1

The answer is `=125(cos45+isin45)`

Explanation:

DeMoivre theorem states that
`(costheta+isintheta)^n=cosntheta+isinntheta`
and `e^(itheta)=costheta+isintheta`
Here we have `5e^(15i)=5(cos15+isin15)`
`:.(5e^(15i))^3=5^3(cos15+isin15)^3`
`=125(cos45+isin45)`