1. The problem statement, all variables and given/known data This is an example in Advanced Engineering Mathematics by Erwin Kreyszig p.675 which I dont understand. If you map [tex]w=z^2[/tex] using Cartesian Co-ordinates, w is defined as [tex]w=u(x,y)+iv(x,y)[/tex], therefore, [tex]u=Re(z^2)=x^2-y^2[/tex] and [tex]v=Im(z^2)=2xy[/tex]. The function is graphed using u and v as the axes, and a line x=c is graphed as a parabola as is the like y=k. What I want to understand is, that is this so because the surface we were graphing these lines on (which was the xy plane) has been warped in such a manner as to define a new plane uv so that the projection of the lines x=c and y=c, on this uv plane turns out to be a parabola? Is that so?