How to Prove a Complex Inequality with Complex Algebra

[Dinheiro]

Homework Statement

Let b and a be two complex numbers. Prove that
|1+ab| + |a + b| ≥ √(|a²-1||b²-1|).

Homework Equations

Complex algebra

The Attempt at a Solution

I don't know how to proceed. I posted it here to get some ideas :p

 

[jbunniii]

Try factoring the left hand side:
$$|a^2 - 1||b^2 - 1| = |(a-1)(a+1)(b-1)(b+1)|$$
Now see what happens if you rearrange the factors and recombine them.