TITLE: Visualising functions from complex numbers to complex numbers
QUESTION [10 upvotes]: I think that complex analysis is hard because graphs of even basic functions are 4 dimensional. Does anyone have any good visual representations of basic complex functions or know of any tools for generating them?

REPLY [2 votes]: Oh yes, there's a way to do this. Here is my exploration into the topic about a month ago using Mathematica. The easiest thing to do is to plot the vector field and let the direction of the arrows represent the phase and let the color represent the magnitude. This is a great way to get all four dimensions on a plane and I think it's very enlightening.
https://mathematica.stackexchange.com/questions/4244/visualizing-a-complex-vector-field-near-poles