Complex inequality with absolute values

1. Oct 18, 2011

Grothard

1. The problem statement, all variables and given/known data

Determine the values of $z \in \mathbb{C}$ for which $|z+2| > 1 + |z-2|$ holds.

2. Relevant equations

Nothing complicated I can think of.

3. The attempt at a solution

For real values this holds for anything greater than $1/2$. If I could figure out the boundaries of the area I'd be set, but the triangle inequality doesn't return anything nontrivial here. Tedious expansion into real and imaginary terms could be a solution, but there's probably a better way.

2. Oct 19, 2011

Grothard

I've found out through wolfram alpha that the inequality holds for an area enclosed by two crossing lines. Not quite sure where to get the two lines from