1. The problem statement, all variables and given/known data If f(z) is analytic at a point Zo show that the Conjugate(f(z conjugate)) is also analytic there. (The bar is over the z and the entire thing as well.) 3. The attempt at a solution I know if a function is analytic at Zo if it is differentiable in some neighborhood of Zo. I also know the Cauchy Riemann equations would hold there. I also know that the partial with respect to Z conjugate is zero. I guess I am having trouble with the double conjugation here and what kind of formal argument to make.