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

##### 1 Answer
Dec 29, 2015

Apply Euler's formula to convert the function into a trigonometric form, and then evaluate to find

$5 {e}^{\frac{3 \pi}{2} i} = - 5 i$

#### Explanation:

Using Euler's formula: ${e}^{i \theta} = \cos \left(\theta\right) + i \sin \left(\theta\right)$

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

$= 5 \left(0 + i \left(- 1\right)\right)$

$= - 5 i$