There is a whole lot easier a way to understand what the DFT does which doesn't involve complex things.

If you really believe this, try to generate a discrete Fourier transform without using complex numbers of one kind or another. It can't be done. Typically, scalars are (and must be) placed in s complex context (i.e. each term with a zero imaginary part) for the process to succeed.

> The second table is the same as the first except that sampled cosinusiods (the quaduratures) are used instead of sinusoids.

Ah. I see you proved my point. I should have read ahead. Your cosines are the imaginary terms, each 90 degrees away from their partners.