Problem 1722 (difficulty: 5/10)

a) \(\displaystyle \displaystyle \int\limits_{|z-i|=1} \frac{e^{iz}}{1+z^2}dz=?\)  b) \(\displaystyle \displaystyle \int\limits_{|z-\pi|=1} \frac{e^{z}}{\sin^2 z}dz=?\)  c) \(\displaystyle \displaystyle \int\limits_{|z-2\pi i|=1} \frac 1{e^{z}-1}dz=?\)  d) \(\displaystyle \displaystyle \int\limits_{|z|=\pi} \frac{e^{z}}{\cos z-1}dz=?\)

Give me another random problem!