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    Singularities, Convergence of Taylor Series, Residues and Contour Integral

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    Consider the complex function:

    f(z) = 1/(z^2 + z + 1)(z + 5i)

    a) Find and classify the singularities of f(z);
    b) Without finding the series explicitly, determine the region of uniform convergence of the Taylor series taken about the origin;
    c) Find the residues of f(z) at each of the singular points;
    d) Find the value of the contour integral - Integral(c) f(z)dz, where C i the circle x^2 + y^2 = 9.

    © BrainMass Inc. brainmass.com October 5, 2022, 6:16 pm ad1c9bdddf
    https://brainmass.com/math/real-analysis/singularities-convergence-of-taylor-series-residues-and-contour-integral-170579

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

    © BrainMass Inc. brainmass.com October 5, 2022, 6:16 pm ad1c9bdddf>
    https://brainmass.com/math/real-analysis/singularities-convergence-of-taylor-series-residues-and-contour-integral-170579

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