Exercise 6.  Express the following quantities in  [Graphics:Images/ComplexFunTrigModHome_gr_300.gif]  form.  

6 (a).   [Graphics:Images/ComplexFunTrigModHome_gr_301.gif].  

Solution 6 (a).

See text and/or instructor's solution manual.

Answer.   [Graphics:../Images/ComplexFunTrigModHome_gr_302.gif]

Solution.  Use identity (5-35)   [Graphics:../Images/ComplexFunTrigModHome_gr_303.gif]   and get  

                    [Graphics:../Images/ComplexFunTrigModHome_gr_304.gif]     

We are done.   

                    [Graphics:../Images/ComplexFunTrigModHome_gr_305.gif]          [Graphics:../Images/ComplexFunTrigModHome_gr_306.gif]

                    The point  [Graphics:../Images/ComplexFunTrigModHome_gr_307.gif]  and it's image  [Graphics:../Images/ComplexFunTrigModHome_gr_308.gif].  

We are really done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexFunTrigModHome_gr_309.gif]

[Graphics:../Images/ComplexFunTrigModHome_gr_310.gif]


[Graphics:../Images/ComplexFunTrigModHome_gr_311.gif]

[Graphics:../Images/ComplexFunTrigModHome_gr_312.gif]



















This solution is complements of the authors.



































 

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