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RE: My identity is complex
Good job in spotting that mistake! Thanks. I made adjustments. To avoid talking about signs I identified it to a part of the imaginary axis.
Well there is of course lots of nice math that you can apply on the complex plane which makes use of the underlying symmetry (like everything related to singularities). Once you know this math things get easier :)
I hope you will continue posting. My preferred application is the residue theorem. This is a so wonderful piece of math! :)