# How can you use trigonometric functions to simplify  27 e^( ( pi)/2 i )  into a non-exponential complex number?

Dec 24, 2015

Use the equation ${e}^{i \theta} = \cos \left(\theta\right) + i \sin \left(\theta\right)$ to find
$27 {e}^{\frac{\pi}{2} i} = 27 i$

#### Explanation:

Using the identity ${e}^{i \theta} = \cos \left(\theta\right) + i \sin \left(\theta\right)$ we have

$27 {e}^{\frac{\pi}{2} i} = 27 \left(\cos \left(\frac{\pi}{2}\right) + i \sin \left(\frac{\pi}{2}\right)\right)$

$= 27 \left(0 + i \left(1\right)\right)$

$= 27 i$