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Contour integral over upper half circle

University · ●●○○○ 20 pts

Find ∫C(1+2z) dz\int_C \left(1+\frac{2}{z}\right)\,dz, where CC is the upper unit half-circle C(θ)=eiθC(\theta)=e^{i\theta}, 0≤θ≤π0 \le \theta \le \pi, traversed from z=1z=1 to z=−1z=-1. Give the real part and the imaginary part of the result separately. Round the imaginary part to two decimal places.

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complex line integralscontour integration