Exercise 13.  From Exercise 12 and basic cancellation laws, it follows that  [Graphics:Images/ComplexAlgebraModHome_gr_255.gif].  
The numerator here,  [Graphics:Images/ComplexAlgebraModHome_gr_256.gif],  is trivial to calculate and, as the denominator   [Graphics:Images/ComplexAlgebraModHome_gr_257.gif]  is a real number (see Exercise 3), computing the quotient  [Graphics:Images/ComplexAlgebraModHome_gr_258.gif]  should be rather straightforward.  
Use this fact to compute  [Graphics:Images/ComplexAlgebraModHome_gr_259.gif]  if  [Graphics:Images/ComplexAlgebraModHome_gr_260.gif]  and again if  [Graphics:Images/ComplexAlgebraModHome_gr_261.gif].

Solution 13.

See text and/or instructor's solution manual.

For [Graphics:../Images/ComplexAlgebraModHome_gr_262.gif],  

        [Graphics:../Images/ComplexAlgebraModHome_gr_263.gif]  

For [Graphics:../Images/ComplexAlgebraModHome_gr_264.gif],  

        [Graphics:../Images/ComplexAlgebraModHome_gr_265.gif]  

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexAlgebraModHome_gr_266.gif]
[Graphics:../Images/ComplexAlgebraModHome_gr_267.gif]

and

[Graphics:../Images/ComplexAlgebraModHome_gr_268.gif]
[Graphics:../Images/ComplexAlgebraModHome_gr_269.gif]
















 

This solution is complements of the authors.















 














 

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