Question

Show that an analytic function with a constant real part is constant

Answer 1

Answer:

Theorem: Let f(z) = u + iv be an analytic function. 1. If f (z) is identically zero, then f(z) is a constant. ... For example, if f (z) = 0, then 0 = f (z) = ∂u ∂x + i ∂v ∂x .