Question

Find integral: int(dz/z) on curve C={z=x+iy| abs(z)=1, y>=0}

Answer 1

$$z = e^{it}$$ $$\int_{C} \frac{dz}{z} = \int_{0}^{\pi} \frac{ie^{it}}{e^{it}} dt = \int_{0}^{\pi} idt = \pi i$$