# How can you use trigonometric functions to simplify  3 e^( ( 11 pi)/6 i )  into a non-exponential complex number?

Sep 18, 2016

$\frac{3 \sqrt{3}}{2} - \frac{3}{2} i$

#### Explanation:

Use Euler's formula ${e}^{i x} = \cos x + i \sin x$

$3 {e}^{\frac{11 \pi}{6} i} = 3 \left(\cos \left(\frac{11 \pi}{6}\right) + i \sin \left(\frac{11 \pi}{6}\right)\right)$

$3 {e}^{\frac{11 \pi}{6} i} = 3 \left(\frac{\sqrt{3}}{2} + i \left(- \frac{1}{2}\right)\right)$

$3 {e}^{\frac{11 \pi}{6} i} = \frac{3 \sqrt{3}}{2} - \frac{3}{2} i$