I wonder what the plot of , with looks like?
It's a 2-dimensional surface inside a four dimensional , so to visualize it, we need to map it to somehow.
How? There are of course many ways, so let's just do one arbitrary way first, e.g., setting the imaginary part of the second complex number to 0, i.e., we are projecting to that space...
In any case, the surface in is
So the equations of the surface in is:
Hmmm, it's tempting to eliminate one variable, and end up with a surface in , so might as well do that. We have so
Multiply through by :