Complex Number Proof of $\overline{\left(\frac {z_1}{z_2}\right)}=\frac {\overline{z_1}}{\overline{z_2}}$. 
Let $z_1=a_1+b_1i$ and $z_2=a_2+b_2i$ be complex numbers. Let $\overline{z_1}$ and $\overline{z_2}$ be the conjugate of $z_1$ and $z_2$, respectively. Prove: $$\overline{\left(\frac {z_1}{z_2}\right)}=\frac {\overline{z_1}}{\overline{z_2}}$$

My Attempt:
I started with $\overline{\left(\frac {z_1}{z_2}\right)}$ and multiplied it by $\frac {z_1}{z_2}$ to get $\left|\frac {z_1}{z_2}\right|^2=\frac {a_1^2+b_1^2}{a_2^2+b_2^2}$, but now, I don't know where to continue afterwards.

Hint:
You can complete your proof multiplying also the RHS by $\frac{z_1}{z_2}$ then show that  $\left|\frac {z_1}{z_2}\right|=\frac{|z_1|}{|z_2|}$ ( easy in polar form).
