What are the complex numbers, really?
I'm wary of anyone who tries to explain complex numbers without pictures. The best explanation of complex numbers that I've ever seen is <a href="http://acko.net/blog/how-to-fold-a-julia-fractal/" rel="nofollow">http://acko.net/blog/how-to-fold-a-julia-fractal/</a>. I wish that explaination existed when I was struggling with my Electrical Engineering classes in college.