Problem 1677 (difficulty: 4/10)

Let \(\displaystyle \Gamma\) be the curve shown in the figure.

(a) Compute \(\displaystyle \displaystyle \int\limits_\Gamma \frac{z^{20}+2}{z^2-1} \dz\).

(b) Compute \(\displaystyle \displaystyle \int\limits_{C(0, 1)} \frac {\sin z} z \dz\).

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