# How can you use trigonometric functions to simplify  19 e^( ( 5 pi)/3 i )  into a non-exponential complex number?

##### 1 Answer
Apr 14, 2016

I found: $9.8 - 16.4 i$

#### Explanation:

We can use Euler Form of the complex number and the conversion into trigonometric form to get to the normal $a + i b$ form as:
$19 {e}^{\left(\frac{5}{3} \pi\right) i} = 19 \left[\textcolor{red}{\cos \left(\frac{5}{3} \pi\right) + i \sin \left(\frac{5}{3} \pi\right)}\right] =$
evaluating our trig forms we get:
$= 19 \left[0.5 - 0.866 i\right] = 9.8 - 16.4 i$