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    (last question I swear! :rolleyes: )

    So I've got z\bar{z} and I need to show that it's nowhere differentiable on D(1;\frac{1}{2}).

    I thought of parametrising using \phi(t) = 1 + e^{it} then using \displaystyle\lim_{h\to 0} \dfrac{f(z+h)-f(z)}{h} to show that the limit isn't uniquely defined, but this seems messy and flawed (since I think I'm only proving this on the disc rather than inside it).

    Using CR eqns I'd be proving it, but I wouldn't be proving it specifically for the given disc... any suggestions?

    Using CR you can prove it for everywhere except 0. (And since 0 isn't in your disc, you've proved it for your disc).
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