ComplexPlot3D

ComplexPlot3D[f, {z, zmin, zmax}] generates a three-dimensional plot of Abs[f] over the complex rectangle with corners zmin and zmax, with the surface colored by Arg[f].

Examples

Plot the magnitude of a complex function:

ComplexPlot3D[z^2, {z, -2 - 2 I, 2 + 2 I}]

Visualize a function with singularities:

ComplexPlot3D[1/z, {z, -2 - 2 I, 2 + 2 I}]

Plot a more complex function:

ComplexPlot3D[(z^2 - 1)/(z^2 + 1), {z, -2 - 2 I, 2 + 2 I}]

Please visit the official Wolfram Language Reference for more details.