# How can you use trigonometric functions to simplify  9 e^( ( 3 pi)/4 i )  into a non-exponential complex number?

Apr 1, 2016

$= 9 \left(- \frac{\sqrt{2}}{2} + i \frac{\sqrt{2}}{2}\right)$
${e}^{i x} = \cos x + i \sin x$
$9 {e}^{\frac{3 \pi}{4} i} = 9 \left(\cos \left(\frac{3 \pi}{4}\right) + i \sin \left(\frac{3 \pi}{4}\right)\right)$
$= 9 \left(- \frac{\sqrt{2}}{2} + i \frac{\sqrt{2}}{2}\right)$