Example 10.12.  The transformation    is a one-to-one conformal mapping of the vertical strip    onto the disk  .  

Figure 10.16  The composite transformation  .

Explore Solution 10.12.

Enter the function  f(z) = tan(z).  

Using the trigonometric identities

We obtain the following form for  f(z) = tan(z).  

Which is the same as the following function  .  

The first function in this composition is  ,  and the second function is a bilinear transformation ,  and then  .

The image is traced using a graph.

We see that the transformation  w = tan(z)  maps the vertical strip    onto the disk  .  

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