9 (b).  Use    in part (a) and    and verify the computation:

                         .  

Solution 9 (b).

See text and/or instructor's solution manual.

      Use    and in the computation:

                      

We are done.   

Aside.  We can let Mathematica double check our work.

Maple can check our work too!

     > V1 := limit( (z+1)*z^(1/3)/(z^3*(z+1)), z=-1);

               

     > evalc( 2*Pi*I/(1-exp(I*2*Pi/3))*V1 );

               

This solution is complements of the authors.

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