area plotting in the complex plane

Does anybody know how to "plot" an area in the complex plane? For example

{z:|f(z)|<1} where f(z)=(1+z)/(1-z).

Or more generally, f(z) is a complex function.

P.S. Shaded area may be preferable.

Answer 1

[Walter Roberson]

What kind of representation were you hoping for? For example can you use the change of variables z = p + q*1j, use p as one axis, q as another axis, and then use isosurfaces on the resulting 4 dimensional plot (the other two axes being real(f(z)) and image(f(z))) ?

[jack]

I think two dimension is enough. For instance, plot in the complex plane the area {z:|f(z)|<1} where f(z)=(1+z)/(1-z) and z=x+iy. Actually the curve |f(z)|=1 is not hard to plot by plotting the implicit function.

Is there any function for plotting a "open set" in MATLAB?