# How can you use trigonometric functions to simplify  15 e^( ( pi)/3 i )  into a non-exponential complex number?

May 16, 2016

$15 {e}^{\frac{\pi}{3} i} = \frac{15}{2} + \frac{15 \sqrt{3}}{2} i$

#### Explanation:

We will use Euler's formula:

${e}^{i \theta} = \cos \left(\theta\right) + i \sin \left(\theta\right)$

With that, we have

$15 {e}^{\frac{\pi}{3} i} = 15 \left(\cos \left(\frac{\pi}{3}\right) + i \sin \left(\frac{\pi}{3}\right)\right)$

$= 15 \left(\frac{1}{2} + \frac{\sqrt{3}}{2} i\right)$

$= \frac{15}{2} + \frac{15 \sqrt{3}}{2} i$