8-2 4. Let g(z) = = and let C be the complex contour |z| = 3, taken counterclockwise. z² +4' (a) Carefully explain why n

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8 2 4 Let G Z And Let C Be The Complex Contour Z 3 Taken Counterclockwise Z 4 A Carefully Explain Why N 1 (212.84 KiB) Viewed 17 times

8-2 4. Let g(z) = = and let C be the complex contour |z| = 3, taken counterclockwise. z² +4' (a) Carefully explain why neither Cauchy's integral theorem nor Cauchy's integral formula (without ho- motoping) can be used to determine $ 9(2) dz. (b) Use partial fractions on g(z) to convert it to a form where one of the above methods is applicable, and use that method to determine the value of the contour integral. (c) Using knowledge from §5.4 in your textbook, is it possible to determine the value of the integral if C is instead defined by (i) |z| = 1, or by (ii) |z| = 2? (If not, what is the issue?)