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.
References in periodicals archive ?
By Rouche's Theorem, the transcendental equation (i) has roots with positive real parts if and only if it has purely imaginary roots.
An application of the principle of the argument or Rouche's Theorem shows such a root to exist with all other roots of modulus greater than 3/4.
One involves control over derivatives and/or complex analyticity which will allow uniqueness via an appeal to an intermediate value theorem or a use of Rouche's theorem.