# What is the trigonometric form of 5e^(pi i) ?

Jan 23, 2016

$5 \left[\cos \left(\pi\right) + i \sin \left(\pi\right)\right]$

#### Explanation:

Euler's theorem states that : ${e}^{i \theta} = \cos \theta + i \sin \theta$

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

Note : since $\cos \left(\pi\right) = - 1 \mathmr{and} \sin \left(\pi\right) = 0$

the expression may be simplified to - 5