# How can you use trigonometric functions to simplify  25 e^( ( 2 pi)/3 i )  into a non-exponential complex number?

$25 {e}^{\frac{2 \pi}{3} i} = - \frac{25}{2} + 25 i \frac{\sqrt{3}}{2}$
$r {e}^{i \theta} = r \left(\cos \theta + i \sin \theta\right)$
$25 {e}^{\frac{2 \pi}{3} i} \to r = 25 , \theta = \left(\frac{2 \pi}{3}\right)$
$25 {e}^{\frac{2 \pi}{3} i} = 25 \left(\cos \left(\frac{2 \pi}{3}\right) + i \sin \left(\frac{2 \pi}{3}\right)\right)$
$25 {e}^{\frac{2 \pi}{3} i} = 25 \cos \left(\frac{2 \pi}{3}\right) + 25 i \sin \left(\frac{2 \pi}{3}\right)$
$25 {e}^{\frac{2 \pi}{3} i} = - \frac{25}{2} + 25 i \frac{\sqrt{3}}{2}$