Imaginary Numbers Real? Yes, You Just Need to Rotate Your Mind!

The whole sqrt(-1) imaginary number thing has always been pretty abstract to me (and probably most others who learned them, but then never had to use them in their job or anything).

A Visual, Intuitive Guide to Imaginary Numbers gives one a technique to visualize them and how and why they work the way they do, and also demonstrates how imaginary numbers can be surprisingly effective in unexpected areas.