Example 10.12. The transformation w = tan(z) is a one-to-one
conformal mapping of the vertical strip |x| < onto the disk |w| < 1.

The function is .

Which is the same as the function .

The first function in this composition is .

The image is traced using a graph.

 Thus, the image of the vertical strip |x| < is the disk |w| < 1.

Return to the Complex Analysis Project  

(c) John Mathews, 1998, 2006