Let $u=\Re(z^n)$. Now I want to see the set $$ A=\{z:u(z)=u(0)=0\}=\{z=re^{i\theta}:r^n\cos(n\theta)=0\}. $$ Now I don't know how to prove the following statement (highlighted). Basically why does the set $A$ looks like $m$ lines passing through $0$ and intersecting with equal $\pi/n.$
