Labels:circle | graphics | graphic design | art OCR: Figure 12-6: Illustration of the Range of the Function (z - 1)/(z +1) A line is a degenerate circle with infinite radius; when I say "circles" here I also mean lines. Then (z - 1)/(z + 1) maps circles into circles. All circles through -1 become lines; all lines become circles through 1. The real axis is mapped onto itsell; 1 to the origin, the origin to -1, - 1 to infinity, and infinity to 1. The imaginary axis becomes the unit circle; ; is mapped to itaell, as is -i. Thus the entire right half-plane is mapped to the interior of the unit circle, the unit circle interior to the left half-plane, the left half-plane to the unit circle exterior, and the unit circle exterior to the right half-plane. Imagine the complex plane to be a vaat sea. The Colossus of Rhodes straddles the origin, ita left foot on ; and its right foot on -i. It bends down and briefly paddles water between ita lega ao furiously that the water directly beneath is pushed out into the entire area behind it; much that was behind swirls forward to either side; and all that was before is sucked in to lie between ity feel.
