Question: Do the following integrals: a. (oint_{|z-i|=3} frac{e^{z}}{z^{2}+pi^{2}} d z) b. (oint_{|z-i|=3} frac{z^{2}-3 z+4}{z^{2}-4 z+3} d z). c. (int_{-infty}^{infty} frac{sin x}{x^{2}+4} d x). [This is (operatorname{Im}
Do the following integrals:
a. \(\oint_{|z-i|=3} \frac{e^{z}}{z^{2}+\pi^{2}} d z\)
b. \(\oint_{|z-i|=3} \frac{z^{2}-3 z+4}{z^{2}-4 z+3} d z\).
c. \(\int_{-\infty}^{\infty} \frac{\sin x}{x^{2}+4} d x\). [This is \(\operatorname{Im} \int_{-\infty}^{\infty} \frac{e^{i x}}{x^{2}+4} d x\).]
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