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