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

Mar 28, 2016

$\frac{25}{2} + \frac{25}{2} \sqrt{3} i$

#### Explanation:

As ${e}^{i \theta} = \cos \theta + i \sin \theta$, we have

$25 {e}^{\frac{\pi}{3} i} = 25 \cos \left(\frac{\pi}{3}\right) + i 25 \sin \left(\frac{\pi}{3}\right)$ or

$25 \times \frac{1}{2} + 25 \times \frac{\sqrt{3}}{2} i$ or

$\frac{25}{2} + \frac{25}{2} \sqrt{3} i$