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