[Math] Find all complex numbers satisfying the equation

Question

Find all complex numbers $z$ satisfying the equation $$\left|z+\frac{1}{z}\right|=2.$$

Answer 1

Write that $z+\frac{1}{z} = 2e^{i\theta},\ \theta \in \mathbb{R}$

then multiply both sides by $z$, and solve the 2nd degree equation in $z$: $$z^2-2e^{i\theta}z+1=0$$