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    Mathematics - Complex Variables

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    Suppose w = f(z) is analytical in C.Show that its real and imaginary parts satisfy the Cachy-Riemann equations.

    Please show all steps to this proof .

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    Solution Preview

    The solution file is attached.

    Suppose w = f(z) = u(x, y) +  v(x, y) is analytic on an open set S. Then it is differentiable at every point z of S so that Lim (z  0) [f(z + z) - f(z)]/z exists and the limit is independent of the path along which z  0.
    Let z = x +  y. Then f(z + z) = u(x + x, y + y) +  v(x + x, ...

    Solution Summary

    Complex variable analytics is analyzed. A complete, Neat and Step-by-step Solution is provided in the attached file.