Question

How do I find the polar form of `a+bi`?

Answer 1

I presume we're looking for a radius `r` and angle `theta` such that `a + bi = r(cos theta + i sin theta)`.

Pythagoras theorem gives us `r = sqrt(a^2+b^2)`.

Simple trigonometry gives us `tan theta = b/a`, so `theta = arctan (b/a)`.