state and prove Cauchy Riemann equation
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If u and v satisfy the Cauchy-Riemann equations, then f(z) has a complex derivative. The proof of this theorem is not difficult, but involves a more careful understanding of the meaning of the partial derivatives and linear approxi- mation in two variables. ∇v = (∂v ∂x , ∂v ∂y ) = ( − ∂u ∂y , ∂u ∂x ) .
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