Question: 
If we say that $\gamma_1$ is the straight line from $-2 + 2i$ to $-1$, I get $\gamma_1$ = some function of $t_1$ for $t_1$ goes from $0$ to $1$.
Then I need to get the parameterization for the clock-wise half circle. I get $\gamma_2$ = some function$(t_2)$. However, I don't know how to get the domain for $t_2$. My guess is going from $3\pi+2k\pi$ to $2pi +2k\pi$ for $k \in \mathbb{R}$ because of the following reason:
- If $k_2$ goes from $\pi$ to $0$, then $\gamma(t)= \gamma_1(t_1)$ or $\gamma_2(t_2)$ has two values for when $t =$, let's say, $\frac{\pi}{6}$.
Is my domain for $k_2$ correct?