Use the Cauchy Riemann equations to prove the following: (a) If f(z) = u(x, y) +...

 

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Use the Cauchy Riemann equations to prove the following: (a) If f(z) = u(x, y) + iv(x, y) is a regular function for which u + v is a constant, then f(z) is a constant. (b) If f(z) = u(x, y) + iv(x, y) is a regular function then 2 a) (1/(-1) + - ((-1) = 2 2 df dz B) 2 + 2 2 2 =) | (2) | = 4 | 2 Use the Cauchy Riemann equations to prove the following: (a) If f(z) = u(x, y) + iv(x, y) is a regular function for which u + v is a constant, then f(z) is a constant. (b) If f(z) = u(x, y) + iv(x, y) is a regular function then 2 a) (1/(-1) + - ((-1) = 2 2 df dz B) 2 + 2 2 2 =) | (2) | = 4 | 2