# What is the polar form of -2 + 9i?

Jun 25, 2018

Polar form is given by ${\rho}_{\theta}$ where $\rho = \left\mid z \right\mid$ and $\theta$ is the angle formed by complex number and x-axis

First we draw the complex number in coordinate axis system and notice that the angle is bigger than 90 degrees

$\left\mid z \right\mid = \sqrt{4 + 81} = \sqrt{85}$

And $\tan \alpha = \frac{2}{9}$ where $\alpha$ is angle formed by complex and y-axis, then we will add this angle to 90 degrees

alpha=12º 31´ and theta=alpha+90=102º 31´

The number in polar form is sqrt85_(102º,31´)