# Polar coordinate

by teng125
Tags: coordinate, polar
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,552 Polar form of the number a+ bi is either $r(cos\theta+ i sin\theta)$ or $r e^{i\theta}$ (since $e^{i \theta}= cos\theta+ i sin\theta$ they are equivalent) where r is |a+ bi| and $\theta$ is the "argument" or angle the line through (0,0) and (a,b) makes with the positive real axis. For a+ bi, $r= \sqrt{a^2+ b^2}$ and $\theta= arctan(\frac{b}{a})$ as long as a is not 0. If a is 0 and b is positive, then $\theta= \frac{\pi}{2}$. If a is 0 and b is negative, then $\theta= -\frac{\pi}{2}$. The number 0 (0+ 0i) cannot be written in "polar form". If you were given a problem requiring the answer in polar form, surely you were already taught all of that?