Math Help - Complex numbers inequality

1. Complex numbers inequality

prove that

$|z_1|^2 + |z_2|^2 + |z_1 + z_2|^2 \ge \frac{ 2(|a\cdot z_1 + b\cdot z_2|^2)}{(a^2 + b^2)}$

$z_1$ and $z_2$ are complex numbers and a and b are non zero real numbers

2. Try $z_1=i,\ z_2=-i,\ a=1,\ b=-1.$