Recent content by Daized

Actually managed to figure it out just about Assume that f(z) = u(x,y) + i v(x,y). We know that u(x, y) = ϕ(v(x, y)). By Cauchy-Riemann, we have ∂u/∂x = ∂v/∂y ==> ϕ'(v(x,y)) * ∂v/∂x = ∂v/∂y, and ∂u/∂y = -∂v/∂x ==> ϕ'(v(x,y)) * ∂v/∂y = -∂v/∂x. Substituting the first equation into...

Homework Statement Let f(z) be an analytic function in the complex plane ℂ, and let \phi be amonotonic function of a real variable. Assume that U(x,y) = \phi(V(x,y)) where U(x,y) is the real part of f(z) and V(x,y) is the imaginary part of f(z). Prove that f is constant. Homework Equations...