# How do I go about graphing the region, \$Re(z^2)>1\$ in the Complex Plane?

The questions asks to describe the region, $$Re(z^2)>1$$, graphically in the complex plane. The math is fairly simple. If we let $$z=x+iy$$, then $$z^2=(x+iy)(x+iy)\z^2=x^2-y^2+i(2xy)$$

Hence the $$Re(z^2)=x^2-y^2>1$$

Graphically speaking, this function sketches a hyperbola in the real $$xy$$ plane. However, my confusion is that the question asks to represent $$Re(z^2)>1$$ in the complex plane. How can I go about representing the real part of a function in the complex plane?