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06-06-2023
Mathematics

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Using the limit definition of the derivative, prove that f(z) = |z|² is C-differentiable if and only if z = 0. Where is f analytic? (Hint: for the first part, expanding |z+Az|² = (z+Az) (z+Az) may help you simplify the differ- ence quotient. The fact |Az|2/Az = Az is also useful.)

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