# How can you use trigonometric functions to simplify  3 e^( ( 3 pi)/8 i )  into a non-exponential complex number?

Feb 19, 2016

we can use Euler's formula to solve the problem

#### Explanation:

Euler's formula ${e}^{i x} = \cos x - i \sin x$
let $p = 3 {e}^{3 \frac{\pi}{8} i}$
${p}^{2} = 9 {e}^{3 \frac{\pi}{4} i}$
p^2=9e^(3pi/4i)=9(cos(3pi/4)+isin(3pi/4)
p=3sqrt(cos(3pi/4)+isin(3pi/4)
$p = 3 \sqrt{- \frac{1}{\sqrt{2}} + i \frac{1}{\sqrt{2}}}$