Question

Draw a picture of S and specify a function giving the path.

Answer 1

\[S=\left\{ z \epsilon C, \left| z \right| \le 1, im z \ge 0\right\}\]
\[S=\left\{ z \epsilon C, 1 \le \left| z \right| \le 2, 0 \le im( z) \le re(z)\right\}\]