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Residues and Poles : Cauchy Integral Formula (Counterclockwise around a Circle)

Find the value of the integral: {see attachment} taken counterclockwise around the circle
(a) |z - 2| = 2
(b) |z| = 4

Please specify the terms that you use if necessary and clearly explain each step of your solution.


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The Cauchy integral formula is used to find residues. The solution is explained with diagrams. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.