Solution 3.

See text and/or instructor's solution manual.

Solution.  Using the quadratic formula Quadratic Formula in Section 1.5,    to get  

                      

Since both these points    lie outside , the function    is analytic inside and on  ,

hence      by the Cauchy-Goursat Theorem.

                    The points    and    which lie outside the contour  .

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