1. The problem statement, all variables and given/known data If f(z) = u + iv is a holomorphic function on a domain D satisfying |f(z)| = constant, show that f(z) is constant. 2. Relevant equations f(z) = u(z) + y(z)i = u(x,y) + y(x,y)i z = x + yi 3. The attempt at a solution |f(z)| = √u2+v2) = √u(x,y)2+v(x,y)2) I know this is a simple problem, but I'm just not seeing the connection. I'm probably missing some obvious relation/equation to consider.