Exercise 1.  Calculate the following.  

1 (c).  [Graphics:Images/ComplexAlgebraRevisitedModHome_gr_45.gif].  

Solution 1 (c).

See text and/or instructor's solution manual.

Use the general formula  [Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_46.gif].  

For  [Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_47.gif],  use the formula  [Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_48.gif].  

Here we have  [Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_49.gif],  and  [Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_50.gif],  so that

        [Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_51.gif][Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_52.gif].

We are done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_53.gif]

[Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_54.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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