phukraut

conformally equivalent means there is a conformal mapping between the sets in the complex plane. conformal means there is a biholomorphic map.. a holomorphic map f(z) is a function with a complex derivative such that df/dzbar=0. thanks for the help.

i attempted to prove this by contradiction. i assumed there existed a map, then by a compositions of maps from this beginning (a composition of transforms) showed that the end result would have to be something that is NOT conformally equivalent to the first set. this would imply that the only conformal mapping of that set which is of the form in the second set, would have to be the identity map.