# How can you use trigonometric functions to simplify  13 e^( ( pi)/8 i )  into a non-exponential complex number?

##### 1 Answer
Mar 8, 2016

$13 \left[\cos \left(\frac{\pi}{8}\right) + i \sin \left(\frac{\pi}{8}\right)\right]$

#### Explanation:

Using $\textcolor{b l u e}{\text{ Euler's relation}}$

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

here r = 13 and $\theta = \frac{\pi}{8}$

$\Rightarrow 13 {e}^{\frac{\pi}{8} i} = 13 \left[\cos \left(\frac{\pi}{8}\right) + i \sin \left(\frac{\pi}{8}\right)\right]$