I saw the argument for complex differentiation today and I had a question about a 'well known' aspect of the argument. My professor said something like this (at least a version of it): Derivatives on complex variables are defined in the usual way.(adsbygoogle = window.adsbygoogle || []).push({}); However, in the complex plane, delta(z) may approach zero from any direction.

Why???

For the complex derivative to exist, the limiting value must be independent of the direction the derivative is taken in the complex plane.

Why???

Ok, ok. I think that if the first 'Why???' is answered then the second one will be answered too. So what is the deal, what gives the complex plane this property? I suspect this may be anwered by another question, what is the interpretation of the derivative of a complex function?

Sorry, that's a lot of questions but I am completely baffled on this, thanks!

Here is a link to an argument for the differentiation. http://phyastweb.la.asu.edu/phy501-shumway/2001/notes/lec29.pdf [Broken]

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# Complex Differentiation

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