Reading materials and handouts
Studying and doing mathematics:
An excellent series of videos about imaginary numbers and basics of complex analysis.
Here is a website for visualizing some complex functions. Here is another. Here are many views of the complex exponential function.
More on roots of unity, and more on primitive roots.
More on the stereographic projection. And a video illustrating it.
More on the complex log function, with the picture of its imaginary part.
Discussion on why complex analysis is "so nice".
Proof of the Fundamental Theorem of Algebra from Rouché's Theorem.
More on the Bernoulli numbers.
More on the Mercator projection.
Cool site where you can play around with ways of making a map of the Earth with different complex-valued functions.
Here is where you can visualize conformal mappings.