[andars]

I'd say if it depends on how you think about complex numbers. If your understanding of the imaginary unit is limited to "that thing that when you square it you get -1", I agree with you. But if you think of the imaginary unit as the 2-blade in the geometric algebra of R^2, I would argue it is one of the best ways to think about 2D geometry.

[ajkjk]

My point is that almost no one thinks about it that way, and that's the problem. People are content using complex numbers and saying 'it magically' works instead of dealing with the actual structure they want to be using.

[andars]

In that case, I agree with you wholeheartedly.