# Inequality within complex

I step with a inequality and would like to know if it is truth...

$$||(a_1-a_2)^2+i(b_1-b_2)^2||\leq ||a_1^2+ib_1^2||+||a_2^2+ib_2^2||,\quad \forall a_1,a_2\in\mathbb{R}$$.

I tried to prove it but couldn't. Any help will be appreciated.

Try $$a_1=b_1=1$$ and $$a_2=b_2=-1$$.