A complex Complex inequality

1. Aug 4, 2014

Dinheiro

1. The problem statement, all variables and given/known data
Let b and a be two complex numbers. Prove that
|1+ab| + |a + b| ≥ √(|a²-1||b²-1|).

2. Relevant equations
Complex algebra

3. The attempt at a solution
I don't know how to proceed. I posted it here to get some ideas :p

2. Aug 4, 2014

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.