# What is the trigonometric form of 12 e^( ( pi)/2 i ) ?

Dec 23, 2015

$12 i \sin \left(\frac{\pi}{2}\right)$

#### Explanation:

$12 {e}^{\frac{\pi}{2} i}$ is an imaginary number only you see this because $A r g \left(z\right) = \frac{\pi}{2}$ which is on imaginary line only

So $12 {e}^{\frac{\pi}{2} i} = 12 \left(\cos \left(\frac{\pi}{2}\right) + i \sin \left(\frac{\pi}{2}\right)\right) = 12 i \sin \left(\frac{\pi}{2}\right) = 12 i$

This is due to application of Euler's formula : ${e}^{i \theta} = \cos \theta + i \sin \theta = c i s \theta$

You can see the graph