Exercise 2.  Establish the following identities.

2 (c).   .  

Solution 2 (c).

Solution.   Start with   .    

Thus,   .   Multiplying by    and simplifying gives

                      

Taking the multivalued log results in

                      

Therefore,  

Aside.   In calculating the principal value of   ,  Mathematica manipulates this formula as follows:   

                      

We are done.   

Aside.  The principal value of    can be calculated with Mathematica.

This solution is complements of the authors.

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