Exercise 4.  Express    in the form    for the following values of  z.  

4 (f).  .

Solution 4 (f).

See text and/or instructor's solution manual.

Answer.   .  

Solution.    

                      

We are done.   

Aside.  We can let Mathematica check our work.

                                        The point    and it's image  .  

We are really done.   

Aside.  Look what happens if we switch the real and imaginary parts.

Contrast the above solution with  ,  which is obviously different.

                      

We are really really done.   

Aside.  We can let Mathematica double check our work.

                                                            The point    and it's image  .  

This solution is complements of the authors.

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