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Problem 2. Let C be the circle of radius 100, centered at the origin and positively...

Problem 2. Let C be the circle of radius 100, centered at the origin and positively oriented. The goal of this problem is to compute Z C 1 z 2 − 3z + 2 dz.

(i) Decompose 1 z 2−3z+2 into its partial fractions.

(ii) Compute R C1 1 z−1 dz and R C2 1 z−2 dz, where C1 is the circle of radius 1/4, centered at 1 and positively oriented, and C2 is the circle of radius 1/4, centered at 2 and positively oriented.

(iii) Use the Theorem of Section 53 (Cauchy-Goursat Theorem for multiply connected domains) or its Corollary to evaluate R C 1 z 2−3z+2 dz. Explain carefully why the Theorem or the Corollary can be applied.

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