I know this is a bit vague and there's no end to the conformal maps, but I'm just curious which ones you've memorized out of sheer usefulness, particularly if you work in an area related to complex analysis. Which ones should one be able to derive as well?
Which conformal maps should one have memorized?
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complex-analysis
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1Something I never really internalized was the fact that Möbius transformations correspond to [choices of three points](http://en.wikipedia.org/wiki/Möbius_transformation#Specifying_a_transformation_by_three_points). It seems like that could be really useful. – 2012-06-16