Example 2.10.  Show that the image of the open disk    under the linear transformation    is the open disk  .  

Explore Solution 2.10.

Enter the function   .  

Solve for the inverse function, i.e. solve for  z  in terms of  w.  Then find .  

To solve for ,  we use the computations.

Which is the disk    in the w-plane.  Use Mathematica to graph the transformation.

We see that the image of the open disk    under the transformation    is the open disk  .  

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