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Is differentiation in the complex plane the same as that in the reals? In particular do the normal differentiation rules apply in the complex case such that I can just treat a complex map as a real map?

Thanks.

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    I suppose it depends. What are the normal differentiation rules? In general, complex differentiation is better behaved then real differentiation.2012-01-23
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    @mixedmath: Thanks for replying. By "normal differentiation rules" I mean when we are doing the differentiation are we allowed to ignore the fact the $f(z)$ is complex and treat is as some real $f(x)$?2012-01-23

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