Example 10.5.  Find the bilinear transformation  w = S(z)  that maps the points    onto the points  ,  respectively.

Explore Solution 10.5.

Enter the three points and their images and solve for  w = S(z).  

This is equivalent to the formula  ,  and can be verified by a computation.

Check our work and look at the images of  .  

To visualize the mapping  w = S(z)  we will consider a graph.

(c) 2006 John H. Mathews, Russell W. Howell