Solution 1.

Answer.   .

Solution.   Method I.   Use equations (10-13)  and  (10-14).  

(10-13)             ,

(10-14)             .

Here we have    and   .  

Then  

                

Therefore,   .

We are done.   

Solution.   Method II.   Use brute force and solve the equation    for  z  and get

                      

Therefore,   .

We are really done.   

Aside.  We can let Mathematica double check our work.

We are really really done.   

Aside.  As we saw in Example 10.6, the image of the disk    under    is the upper half plane  .  

                                        The image of the disk    under    is the upper half plane  .  

                                        The image of the disk    under    is the disk  .  

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell