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.

Details 5.

Under Construction

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(c) 2008 John H. Mathews, Russell W. Howell