Exercise 1.  Find all values for

1 (a).  .  

Solution 1 (a).

See text and/or instructor's solution manual.

Answer.   .

Solution.   Use formula (5-14)      where     and  .

Calculate      and   ,   where  .  

Then we have  .  

We are done.   

Aside.  We can let Mathematica check our work.

We are really done.   

Aside.  Contrast this solution with the multivalued logarithm  .  

Since  ,  for this problem we have the relation

.   

That is   .  

Aside.  We can let Mathematica double check our work.

                                                            The point   ,     and the principal value   ,    
                                                            and some of the points   .

This solution is complements of the authors.

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