Exercise 1.  Find    for the following values of  z.  

1 (e).  .  

Solution 1 (e).

See text and/or instructor's solution manual.

One solution is obtained by simplifying the quotient   as follows:

        

then

We are done.   

Another solution is obtained by using the formula  ,  where n is an integer.

Since    and   and     and  ,  an argument of   is easily found to be

        

If we choose  ,  then    lies in the interval,  

so the principal value of the argument is found to be

        

We are done.   

Aside.  We can let Mathematica double check our work.

This solution is complements of the authors.

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