Rouche's theorem

Rouche's theorem

[′rüsh·əz ‚thir·əm]

(mathematics)

If analytic functions ƒ(z) and g (z) in a simply connected domain satisfy on the boundary | g (z)| <>z)| , then ƒ(z) and ƒ(z) + g (z) have the same number of zeros in the domain.