# How do you express the complex number in trigonometric form: -2i?

Jun 13, 2016

Reqd. form $= 2 \left(\cos 3 \frac{\pi}{2} + \sin 3 \frac{\pi}{2}\right) .$

#### Explanation:

The complex no. $z = x + i y$ can be expressed in trigo. form $r c i s \theta = r \left(\cos \theta + i \sin \theta\right)$ by using the conversion formula $x = r \cos \theta , y = r \sin \theta , r = \sqrt{{x}^{2} + {y}^{2}} .$
Here, we have, $x = 0 , y = - 2.$
Clearly, $r = 2.$
Next pair of eqns. is $0 = 2 \cos \theta , - 2 = 2 \sin \theta .$
$\therefore \cos \theta = 0 , \sin \theta = - 1.$ $\theta = 3 \frac{\pi}{2}$
$\therefore$Reqd. form $= 2 \left(\cos 3 \frac{\pi}{2} + \sin 3 \frac{\pi}{2}\right) .$