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?