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irony of truth
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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
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?
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?