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2 problems match “complex line integrals”. Clear

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1. Contour integral over upper half circle ●●○○○ 20 ptsFind $\int_C \left(1+\frac{2}{z}\right)\,dz$, where $C$ is the upper unit half-circle $C(\theta)=e^{i\theta}$, $0 \le \theta \le \pi$, traversed from $z=1$ to $z=-1$. Give the real part and the imaginary part of the result separately. Round the imaginary part to two decimal places.
2. Complex line integral of 1/(1+z^2) ●●●○○ 50 ptsEvaluate $\int_1^{1+i}\frac{1}{1+z^2}\,dz$ along the straight line segment from $z=1$ to $z=1+i$. Give the real part and the imaginary part of the result separately. Round each to two decimal places.