I am proving that the function f(z) = Arg z is nowhere differentiable by using the definiton of a derivative. I let z = x + yi. Then, if the limit exists, we have(adsbygoogle = window.adsbygoogle || []).push({});

f'(z) = lim (/\z -> 0) ( f(z + /\z) - f(z) ) / /\z.

(Note that /\ is the triangle symbol)

Also, let /\z = p + iq, where p and q are real values.

Arg z = Tan^-1 (y/x)...how will I continue from here?

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# (Complex Variables) Differentiability of Arg z

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