I just found this linked from Wikipedia, and wanted to share/tag it for myself.

This describes Moebius transformations, which are maps of the complex plane which have the form

for fixed . This video really emphasizes how anything having to do with the complex numbers is really about rotation.

I don’t think we have a plug-in for embedded video yet. Maybe I’ll work on that later. Until then, enjoy the link. [UPDATE: We now have embedded youtube functionality, as can be seen. -- Ed]