Complex inequality with absolute values

[Grothard]

Homework Statement

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

Homework Equations

Nothing complicated I can think of.

The Attempt at a Solution

For real values this holds for anything greater than [itex]1/2[/itex]. 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.

 

[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