Suppose $z\_1 = r\_1(\cos \theta\_1 + i\sin \theta\_1)$ and $z\_2 = r\_2(\cos \theta\_2 + i\sin \theta\_2)$. Prove that $z\_1 = z\_2$ $\iff$ $r\_1 = r\_2 , \theta\_1 = \theta\_2 + 2k\pi$ .

**My try:** The proof for the converse statement is obvious but I don't know how to prove the forward statement. I tried to use "Two complex numbers $a+bi$ and $c+di$ are equal iff $a=b$ and $c=d$, where $a,b,c,d$ are real numbers." but it didn't work.