# How can you use trigonometric functions to simplify  2 e^( ( 5 pi)/3 i )  into a non-exponential complex number?

Mar 15, 2016

$2 \left[\cos \left(\frac{5 \pi}{3}\right) + i \sin \left(\frac{5 \pi}{3}\right)\right]$

#### Explanation:

Using Euler's identity , which states :

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

here r = 2 and $\theta = \frac{5 \pi}{3}$

$\Rightarrow 2 {e}^{5 \frac{\pi}{3} i} = 2 \left[\cos \left(\frac{5 \pi}{3}\right) + i \sin \left(\frac{5 \pi}{3}\right)\right]$