Exercise 3.  Show that    is always a real number.  

Solution 3.

See text and/or instructor's solution manual.

Let    be an arbitrary complex number.  Then  ,  and    ,  which is obviously a real number.

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