Hi, the statement of Inverse Function Theorem for Complex functions I learned is this:
"let f:A->C, g:B->C be continuous s.t. f(A) \subset B. A,B are both open subsets of C, the complex plane. If g(f(z)) = z for all z in A, and g is analytic on f(z) where g'(f(z)) != 0, then f is analytic on...