[aksbhat]

     Complex numbers are a powerful tool for studying the two-dimensional plane: each point corresponds to a unique complex number . The beauty of this correspondence is that it allows you to add, subtract, and multiply points in the plane

I wish someone would have told me this five years ago, it is such a neat way of thinking!

[happy4crazy]

My introductory physics class in college included a problem that investigated the effects of "2d" gravity (a generic attractive force proportional to 1/r instead of 1/r^2) on a point mass in the plane.

When the professor mentioned that I could write all the vectors as complex numbers, and do regular old algebra with them, my brain almost melted.

[cdavid]

if you are interested in new insights about complex numbers and analysis from a geometric POV, this book is wonderful: http://www.amazon.com/Visual-Complex-Analysis-Tristan-Needha... and quite accessible.