# How can you use trigonometric functions to simplify  12 e^( ( 19 pi)/12 i )  into a non-exponential complex number?

Apr 19, 2018

$3 \sqrt{6} - 3 \sqrt{2} - i \left(3 \sqrt{6} + 3 \sqrt{2}\right)$

#### Explanation:

We can turn into $r {e}^{i \theta}$ into a complex number by doing: $r \left(\cos \theta + i \sin \theta\right)$

$r = 12$, $\theta = \frac{19 \pi}{12}$

$12 \left(\cos \left(\frac{19 \pi}{12}\right) + i \sin \left(\frac{19 \pi}{12}\right)\right)$

$3 \sqrt{6} - 3 \sqrt{2} - i \left(3 \sqrt{6} + 3 \sqrt{2}\right)$