Find the connected components of $\displaystyle X = \{(z,w) \in C^2 : z \neq w \}$ with the topology induced from $\displaystyle C^2$.

The trouble with his is that I can't visualise the space X. I tried the same question with $\displaystyle \Re$ instead of $\displaystyle C$ and got the sets $\displaystyle \{(x,y) \in \Re^2 : x > y \}$ and $\displaystyle \{(x,y) \in \Re^2 : x < y \}$, but can't see how to do the "complex version."