I want to sketch the following set:
Set of all those complex numbers which satisfy the following equation $$|z|=arg(z)$$
Efforts:
We are looking at those points in plane whose distance from origin is equal to the angle they subtends with respect to x axis.
arg(z) is multivalued
Points like $(\pi/2,0)$ , $(2\pi,0)$, $(-\pi,0)$ belongs to the set. But what are other points.
How to plot this set.
Thanks for any help.