[lutusp]

> I doubt anyone could make a reply to this comment that would make me feel any better about it.

You may be right, but just to have said it : the Fast Fourier Transform requires complex numbers. One can write a version that avoids complex numbers, but (a) its ugliness gives away what's missing, and (b) it's significantly slower in execution.

Oh -- also --

e^(i Ⲡ) + 1 = 0

Nevertheless, you may be right.