Question

How do you use DeMoivre's Theorem to simplify `(5(cos3.2+isin3.2))^4`?

Answer 1

`(5(cos3.2+isin3.2))^4=625(cos12.8+isin12.8)`

Explanation:

DeMoivre's Theorem states that if we have a complex number

`z=r(costheta+isintheta)`, then

`z^n=r^n(cosntheta+isinntheta)`

Hence `(5(cos3.2+isin3.2))^4`

= `5^4(cos(3.2xx4)+isin(3.2xx4))`

= `625(cos12.8+isin12.8)`