let f, g be analytic on a domain containing a simple closed curve ɣ and its inside. Show that if |f(z)| > |g(z)| for all z in ɣ, then the two equations f(z)=g(z) and f(z)=0 have an equal number of solutions inside ɣ.

I do not know how to prove this T-T plz help me!!!

and use above to determine how many solutions are there for z^3 = z^2 + z + 6 in |z|<1. I know answer for this is "no solution" but why???

plz!!!