Problem 1592 (difficulty: 5/10)

Find the following integrals!

 a) \(\displaystyle \displaystyle\int\limits_{[0, 1+i]} e^z dz\)  b) \(\displaystyle \displaystyle\int\limits_{|z|=1} \frac{1}{z}dz\)  c) \(\displaystyle \displaystyle\int\limits_{|z|=2} \frac{\dz}{z^2 +1}\)

(\(\displaystyle T\) is the square with vertices \(\displaystyle \pm1\pm i\) oriented positively.)

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