Mathematica already has
ComplexPlot3D that plots
ReIm[x, y] against
But what if I wanted to plot my function using an extension of the
x,y,z space? For example, I might have a $f(z) = z^2+1$ and want to plot $w = f(z)$, where $z = x + i y$ and $w = u + i v$, in a more traditional way where the axes are $x,y$ and $u$ and for $v$ I would use colour.
Is this possible?