Let f:C-C be continuous function.If f^2,f^3 be analytic show f is analytic?

note that f^3/f^2 = f except for the points where f(z) = 0 (thos will be singularities). But you can show that those singularities are removable (that will be your job - just remember that the order of the zero of f^3 will be larger than the order of the zero of f^2...) Since they are removable, you can extend this to an entire function. But, this function must be f, since they agree on a set with a limit point (namely, the set of f(z) s.t f(z) is not zero)... We should note that none of this will work if f is constant, but the constant case should be easy, right?

Let f:C-C be continuous function.If f^2,f^3 be analytic show f is analytic?
Divide. Around zeros, use the fact that square roots are multiply defined.