Nice videos! Reminds me of the excellent <i>Visual Complex Analysis</i> by Needham.<p>Just a general warning: one problem with trying to use visualization to help better understand and solve problems involving complex numbers is that this only works in one dimension. While it is easy for us to imagine real spaces up to three dimensions, trying to get an intuition about even a two-dimensional complex space by trying to "visualize" it seems to be so difficult as to be not worth the effort, and all we are left with is formal computational rules. (Incidentally, these rules are not so bad, and thus being able to "see" them at work in one-dimensional case, while helpful in getting comfortable with the idea, quickly loses its importance even in one dimension.)