I'm not sure if it's OK to post this question here or not, the Calculus and Beyond section doesn't really look very heavily proof oriented.(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to prove that if continuous complex valued function f(z) is such that the directional derivatives(using numbers with unit length) preserve angles then the complex derivative exists.

Similarly I need to prove that if the directional derivatives have all the same norm values, then f(z) has a complex derivative.

So far I have proved that if the directional derivative preserves angles then difference quotient from every direction are all linear multiples of each other.

I need now to prove that the norms are the same, I don't know how to link up the norm length with the angles.

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# Directional Derivatives, Complex Variables and the exsistence of a complex derivative

Can you offer guidance or do you also need help?

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