# How can you use trigonometric functions to simplify  9 e^( ( 3 pi)/8 i )  into a non-exponential complex number?

$9 \left[\cos \left(\frac{3 \pi}{8}\right) + i \sin \left(\frac{3 \pi}{8}\right)\right]$
Euler's theorem states : ${e}^{i \theta} = \cos \theta + i \sin \theta$
in this question $\theta = \frac{3 \pi}{8}$
$\Rightarrow = 9 \left[\cos \left(\frac{3 \pi}{8}\right) + i \sin \left(\frac{3 \pi}{8}\right)\right]$