# 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.

https://brainmass.com/math/real-analysis/singularities-convergence-of-taylor-series-residues-and-contour-integral-170579

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