# Rouché’s theorem

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 $C$.

Title Rouché’s theorem RouchesTheorem 2013-03-22 13:35:39 2013-03-22 13:35:39 Johan (1032) Johan (1032) 8 Johan (1032) Theorem msc 30E20