How can a combination of a complex and a real number be plotted in a single graph ? How about merging the Argand and Cartesion planes in perpendicular orientation?

Just use an Argand diagram and take every real number as a complex number with a zero imaginary part, i.e. somewhere on the x axis.

Not sure what you mean by a combination -- sum, product, ordered pair?

 

But a complex function [math]f(z) = w[/math] maps the [math]z[/math]-plane to the [math]w[/math]-plane. So the graph lives in 4-space.

 

What's often done is to show nice color pictures of the real or imaginary parts of a complex function. Here's a page I found but these kinds of pictures are all over the Web.

 

http://www.geom.uiuc.edu/~banchoff/script/CFGExp.html

Edited January 29, 20178 yr by wtf