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

##### 1 Answer
Jul 31, 2016

$\frac{9}{2} + \frac{9 \sqrt{3}}{2} i$

#### Explanation:

We recall that, ${e}^{i \theta} = \cos \theta + i \sin \theta$.

Hence, $9 {e}^{i \frac{\pi}{3}} = 9 \left(\cos \left(\frac{\pi}{3}\right) + i \sin \left(\frac{\pi}{3}\right)\right)$

$= 9 \left(\frac{1}{2} + i \frac{\sqrt{3}}{2}\right)$

$= \frac{9}{2} + \frac{9 \sqrt{3}}{2} i$