Midterm 2 Solutions

Question 1(b)

Question 2(a)

Question 2(b)

Question 2(c)

Question 3(a)

You can do this question even more simply by noting that |z|=1 on C and plugging in |z|=1 right from the start.

Question 3(b)

Question 4(a)

Question 4(b)

Question 5(a)

Question 5(b)

The integrand is analytic everywhere except at z=-2i, which is outside the curve C. So the integrand is analytic everywhere on and inside the closed contour C, and therefore by the Cauchy-Goursat Theorem the integral is zero.

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