Example 5. The conformal mapping . The image of the half-plane is the unit disk .
Figure 2.23 The image of under the mapping .
Figure 2.24 The image of the half disk under is a crescent-shaped region.
Figure 2.25 The images of horizontal and vertical lines under the reciprocal transformation.
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(c) 2008 John H. Mathews, Russell W. Howell