# How can you use trigonometric functions to simplify  24 e^( ( 5 pi)/3 i )  into a non-exponential complex number?

Mar 2, 2016

$24 \left[\cos \left(\frac{5 \pi}{3}\right) + i \sin \left(\frac{5 \pi}{3}\right)\right]$

#### Explanation:

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

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

here r = 24 and $\theta = \frac{5 \pi}{3}$

$\Rightarrow 24 {e}^{\frac{5 \pi}{3} i} = 24 \left[\cos \left(\frac{5 \pi}{3}\right) + i \sin \left(\frac{5 \pi}{3}\right)\right]$