Question

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

Answer 1

Polar form is given by `rho_theta` where `rho=absz` 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

`absz=sqrt(4+81)=sqrt85`

And `tanalpha=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´)`