Complex Line Integral of absolute value of z How do we proceed for the following complex line integral?
$$\int\limits_\gamma |z|\:dz$$
where $\gamma$ is the half circular $|z|=1$, $0\leq \arg (z) \leq \pi$
taking $z=1$ as the initial point.
Any hints would be helpful. Thanks.

Substitute $z = e^{i\theta}$. The limits become $0$ to $\pi$
$|z| = 1$ and $dz$ = $ie^{i\theta}\:d\theta$
$$\int\limits_\gamma |z| \:dz = \int\limits_0^\pi ie^{i\theta} \:d\theta$$
