What is the Locus of Re[z^2]>1?

[Grand]

Homework Statement

Find the locus of $$Re[z^2]>1$$

Homework Equations

The Attempt at a Solution

Subbing in $$z=x+iy$$ gives $$x^2-y^2>1$$, but where do I go from there on. It shouldn't be very tough (i.e. including analysis of functions) because the other examples in the same problem are easy.

 

[Mentallic]

Well can you graph $$x^2-y^2=1$$? It should be clear where it is more than 1 either by intuition or testing some easy points such as (0,0) versus (2,0).
It is the graph of a hyperbola by the way.