Question

Analytic function f(z) constant modulus is constant derivation

Answer 1

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If f(z) is an analytic function with constant modulus, show that f(z) is constant? Write f(z) =u(x,y) + i.v(x,y). As f(z) is analytic, by Cauchy-Riemann conditions, u_x = v_y and u_y = -v_x, where the subscripts denote partial differentiation.

Answer 2

show that an analytic function with constant modulus is constant