I've written up all the equations from this thread together with
detailed step by step derivation:

http://www.theoretical-physics.net/dev/math/complex.html

e.g. the derivatives are here:

http://www.theoretical-physics.net/dev/math/complex.html#complex-derivatives

Most of the examples from this thread are there, but few are still
missing, I'll add them tomorrow.

Bill, please let me know if you have any feedback/comments to it.

Ondrej

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