# How can you use trigonometric functions to simplify  21 e^( ( pi)/2 i )  into a non-exponential complex number?

Mar 3, 2016

$21 {e}^{i \left(\frac{\pi}{2}\right)} = 21 i$

#### Explanation:

There is this identity which is very useful.

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

In this case,

$r = 21$

$\theta = \frac{\pi}{2}$

So plugging the values in

$21 {e}^{i \frac{\pi}{2}} = 21 \left(\cos \left(\frac{\pi}{2}\right) + i \sin \left(\frac{\pi}{2}\right)\right)$

$= 21 \left(\left(0\right) + i \left(1\right)\right)$

$= 21 i$