Question: Let u, v R be two real valued functions defined on an open set C R satisfying the following: (i) All the partial derivatives

Let u, v R be two real valued functions defined on an

Let u, v R be two real valued functions defined on an open set C R satisfying the following: (i) All the partial derivatives of u and u up to second order exist and are continuous at all points of . (ii) The functions u and u satisfy the Cauchy-Riemann equations: v dy du x = 0 du = = Show u and u (both) satisfy Laplace's equation: Ju Ju + x2 y v and Fu x J'v dy = 0.

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