Use the result of Example 4 and properties of stereographic projection to show that the inversion w = 1/z maps any circle in the z-plane to either a circle or a line in the w-plane, and the same holds...

Use the result of Example 4 and properties of stereographic projection to show that the inversion w = 1/z maps any circle in the z-plane to either a circle or a line in the w-plane, and the same holds for the mapping of any line in the z-plane. (Regard 8as a point on every line.)