Extra Example 1.  The transformation    is a one-to-one conformal mapping of the first quadrant    onto the semi-infinite strip  .  

Figure 10.18  The mapping   .  

Explore Solution for Extra Example 1.

Enter the function  f(z) = arcsin(z).  

The image is traced using a graph.

We see that the transformation  w = f(z) = arcsin(z)  maps the first quadrant    onto the semi-infinite strip  .

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