# 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 |