Exercise 1.  Find all values for

1 (g).  .   

Solution 1 (g).

See text and/or instructor's solution manual.

Answer.   ,  where n is an integer.

Solution.   Use formula (5-12)   .  

Calculate      and   ,   where  .     

Then using set notation we write   .  

We are done.   

Aside.  We can let Mathematica check our work.

We are really done.   

Aside.  Contrast this solution with the principal value of the 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