Question: Let f: U C be a complex differentiable function on an open set UC C. Given z EU, calculate the limit of the difference

Let f: U C be a complex differentiable function on an open set UC C. Given z EU, calculate the limit of the difference quotient f'(z) = lim (+2 (S) - f(z) S-2 using values = z+ih where h R. Obtain a formula for f'(z) in terms of the partial derivatives of u = Re(f) and v = Im(f). Calculate the same limit using values (=z + h for h ER.

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