# How can you use trigonometric functions to simplify  16 e^( ( pi)/3 i )  into a non-exponential complex number?

Apr 11, 2016

$8 + 8 \sqrt{3} i$

#### Explanation:

We can use the identity $r {e}^{i \theta} = r \cos \theta + i r \sin \theta$

Hence, $16 {e}^{\frac{\pi}{3} i} = 16 \cos \left(\frac{\pi}{3}\right) + 16 \sin \left(\frac{\pi}{3}\right) i$

= $16 \times \frac{1}{2} + 16 \times \frac{\sqrt{3}}{2} i$

= $8 + 8 \sqrt{3} i$