Explore BrainMass
Share

Explore BrainMass

    Derivative of a ratio of complex functions

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

    Show that the derivative of g(z) exists, and hence g(z) is complex analytic, at points where g(z) does not diverge, thereby proving that the points where g(z) diverges are the only singularities.
    
g(z)= eiz/ z2 +4z+5

    © BrainMass Inc. brainmass.com October 10, 2019, 7:02 am ad1c9bdddf
    https://brainmass.com/math/computing-values-of-functions/derivative-ratio-complex-functions-565410

    Attachments

    Solution Preview

    If the limit (1.1) exists
    (1.1)
    Then is the derivative of the complex function

    Now, assume we have two complex functions and , both differentiable (that is, the limit 1.1 exists for each function)
    We define
    ...

    Solution Summary

    The solution shows how to prove that the derivative of a quotient of two analytic functions exist, and therefore the quotient is analytic as well (except at some points).

    $2.19