Complex variable ( Rouche's Theorem)

Related BrainMass Solutions

• Rouche's Theorem

  315727 Assessing Rouche's Theorem Use Rouche's Theorem to determine the number of zeros, counting multiplicities, of the polynomials inside the given regions.

• Proving the fundamental theorem of algebra by using Rouche's theorem.

  6349 Proving the fundamental theorem of algebra by using Rouche's theorem. How do I prove the fundamental theorem of algebra by using Rouche's theorem? Proof:Suppose the polynomial to be a_0+a_1z+a_2z^2+...

• Complex analysis for Unit Circle

  For |z| = 1 we have |-z| = 1 > |f(z)| So by Rouche's theorem, f(z) - z and z have the same number of zeros in the unit disc; that is, there's exactly one root of f(z) - z inside the unit circle, which in turn corresponds to exactly

• Complex Variables : Analytic Functions, Contours, Polynomials and Rouche's Theorem

  Analytic Functions, Contours, Polynomials and Rouche's Theorem are investigated. The solution is detailed and well presented.

• Complex Analysis / Singularities / Argument Principle : Let f be meromorphic on the region G and not constant; show that neither the poles nor the zeros of f have a limit point in G.

  Note: Rouche's theorem states Suppose (i) G is a simply connected region, (ii) f(z) is meromorphic function in G, (iii) C is a scro curve in G, not passing through a pole or zero of f(z) That's it. Hope you can understand.

• Complex Variables

  By Rouche's theorem, we know that f(z)=a*z^n and f(z)+g(z)=a*z^n-e^z have the same number of zeros, counting with multiplicities, inside C.

• Rouche's formula

  (b) Find the number of the roots of the equation z^6 − 5z^4 + 8z − 1 = 0 in the annulus {z : 1 < |z| < 2} We apply Rouche's theorem in both instances: (a) let p(z) = z^4 - 6z + 3; then for |z| = 2 we have |p - z^4| = |6z - 3

• Residues and Poles; Polar Numbers; Demoivre's Theorem

  36386 Residues and Poles; Polar Numbers; Demoivre's Theorem Please see the attachment for questions relating to residues and poles (polar numbers and Demoivre's Theorem). These problems are from complex variable class.

• Radius of Convergence of the Power Series

  Complex Variable Radius of Convergence of the Power Series