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Rouche's Theorem

Rouché's theorem, named after Eugène Rouché, states that for any two complex-valued functions f and g holomorphic inside some region  with closed contour , if |g(z)| < |f(z)| on , then f and f + g have the same number of zeros inside , where each zero is counted as many times as its multiplicity. 

 Assumption: This theorem assumes that the contour  is simple, that is, without self-intersections.

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