1. The problem statement, all variables and given/known data let f and g be conformal analytic functions with the range of f a subset of the domain of g. Show that the composition g(f(z)) is also conformal. 2. Relevant equations 3. The attempt at a solution Well I know that if the function is conformal it is 1-1, analytic, and its derivative is non zero. So i'm thinking that I would need to show that since f'(z)≠0 and g'(z)≠0 then (g(f(z))'≠0 and then show that since f and g are analytic, g(f(z)) is also analytic. Then the composition will be both analytic and its derivative will not be zero so it will be conformal. Am I working in the right direction?