Question

prove that analytic function with constant real part is constant​

Answer 1

Step-by-step explanation:

If either Ref(z) = u or Imf(z) = v is constant, then f(z) is constant. In particular, a nonconstant analytic function cannot take only real or only pure imaginary values. ... If |f(z)| is constant or arg f(z) is constant, then f(z) is constant. For example, if f (z) = 0, then 0 = f (z) = ∂u ∂x + i ∂v ∂x .