You may be interested in this paper regarding visualizing complex functions:
"Phase Plots of Complex Functions: A Journey in Illustration" by Elias Wegert and Gunter Semmler.
Jim Fowler and I (Steve Gubkin) wrote this webpage to help visualization of complex functions:
We hope to produce an online complex analysis course soon which employs a diverse set of visualization methods. For example, we will use webGL to produce 3d plots of modulus colored by phase, phase plots on the riemann sphere, interactive geometry tools for the poincare metric on the disk, etc. We should also have a lot of computational exercises which are verified directly by a server running an instance of sage. We are still developing back end stuff right now, but we should have something up and running within the year. We do not have anything up there now, but watch this space: http://www.gratisu.org/.