Show that the mapping w 1z maps every straight line to a

Question

Question: 1. Show that the mapping w = 1/z maps every straight line to a circle or straight line, and every circle to a circle or straight line. Give an example of a circle that maps to a line, and a line that maps to a circle.

2. Determine the image of the infinite strip 0 ≤ Imz ≤ 2π under the mapping w = e^z.