Given is function $f(z)=\sin(\pi z)$ and 2 paths $ \gamma_1 :[0,\pi]\mapsto \mathbb C,t\mapsto e^{it}$ , $\gamma_3=\Delta(1+i,-1+i,-i)$. Calculate line integrals and sketch the paths.
I know how to calculate the line integrals but can someone help me with sketches? Is $\gamma_1$ only a half of the circle? What is $\gamma_3$?