Because of restrictions in a print journal I am unable to render complex functions in the plane using a color wheel for the phase of the complex numbers. The best I have been able to come up with is to add contours, in black, of a small set of phase angles, say -3Pi/4, -Pi/4, Pi/4, 3Pi/4.
Here is a typical case of the kind of complex function I am trying to render. First, a plot where I apply Abs[#] to the complex numbers:
This is what I get when I multiply by the function
width = .001;
contours = Table[(a/4.) Pi, {a, -3, 3, 2}];
zeroArgs[a_] := (1 - Exp[-#^2/width]) &[Nearest[contours, a][[1]] - a]
Is there a better option I should know about?