# What is the trigonometric form of 3 e^( ( pi)/2 i ) ?

Mar 2, 2016

$3 i$

#### Explanation:

Trigonometric form of $3 {e}^{\frac{\pi}{2} i}$ can be written as

$3 \times \left(\cos \left(\frac{\pi}{2}\right) + i \sin \left(\frac{\pi}{2}\right)\right)$

But as $\cos \left(\frac{\pi}{2}\right) = 0$ and $\sin \left(\frac{\pi}{2}\right) = 1$, this can be simplified to

$3 \times \left(0 + i \times 1\right)$ or $3 i$