Explore BrainMass

Explore BrainMass

    Complex Variables : Analytic Funcitons and Contours

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Please see the attached file for the fully formatted problems.

    ---
    - Lef f be a function which is analytic inside...
    - Write and equation...
    ---

    (See attached file for full problem description)

    © BrainMass Inc. brainmass.com March 4, 2021, 6:28 pm ad1c9bdddf
    https://brainmass.com/math/complex-analysis/complex-variables-analytic-funcitons-and-contours-45969

    Attachments

    Solution Preview

    Hello there

    Regarding file 80-2, if we pick any point on the curve Gamma, and move that point along the curve once so that it comes back to its original position, we see the tangent moves smoothly through 3 revolutions, so the change in Arg f(z) is 6 Pi radians.

    By the argument principle that the change in arg f = 2 Pi * (Z-P), we see

    Z - P = 3. As f is analytic inside C, it has no poles there, so Z, the no. of zeros, is 3 inside f.

    (Incidentally, the argument principle follows from the result that ...

    Solution Summary

    Analytic Funcitons and Contours are investigated.

    $2.49

    ADVERTISEMENT