Let $f,g$ be analytic on and inside a simple closed curve$C$ Suppose $|f(z)|>|g(z)|$ on $C$ Then $f$ and $f+g$ have the same number of zeros inside $C$
30E20 (Functions of a complex variable :: Miscellaneous topics of analysis in the complex domain :: Integration, integrals of Cauchy type, integral representations of analytic functions)
