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
Canonical name	RouchesTheorem
Date of creation	2013-03-22 13:35:39
Last modified on	2013-03-22 13:35:39
Owner	Johan (1032)
Last modified by	Johan (1032)
Numerical id	8
Author	Johan (1032)
Entry type	Theorem
Classification	msc 30E20