Exercise 5.  Show that, for all z,  

5 (e).  .  

Solution 5 (e).

See text and/or instructor's solution manual.

Solution.   This follows immediately from the identity   ,  

and   ,  

where we replace  .

                      

We are done.   

Aside.  We can let Mathematica double check our work.

We are really done.   

Aside.  We can let Mathematica graph the compositions that are involved.

                                        The composite mappings   ,     ,   

                                        where  .  

                                        The composite mappings   ,     ,   

                                        where  .  
                                        
                                        
                                        
                                        


                                        

                                        The composite mappings   ,     ,   

                                        where  .  

                                        The composite mappings   ,     ,   

                                        where  .  

This solution is complements of the authors.

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