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

6 (e).   [Graphics:Images/ComplexFunTrigModHome_gr_351.gif].  

Solution 6 (e).

See text and/or instructor's solution manual.

Answer.   [Graphics:../Images/ComplexFunTrigModHome_gr_352.gif].  

Solution.  Use identity (5-38)   [Graphics:../Images/ComplexFunTrigModHome_gr_353.gif]   and get  

                    [Graphics:../Images/ComplexFunTrigModHome_gr_354.gif]    
                    
                    [Graphics:../Images/ComplexFunTrigModHome_gr_355.gif]    

We are done.   

                    [Graphics:../Images/ComplexFunTrigModHome_gr_356.gif]          [Graphics:../Images/ComplexFunTrigModHome_gr_357.gif]

                    The point  [Graphics:../Images/ComplexFunTrigModHome_gr_358.gif]  and it's image  [Graphics:../Images/ComplexFunTrigModHome_gr_359.gif].  

We are really done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexFunTrigModHome_gr_360.gif]

[Graphics:../Images/ComplexFunTrigModHome_gr_361.gif]


[Graphics:../Images/ComplexFunTrigModHome_gr_362.gif]

[Graphics:../Images/ComplexFunTrigModHome_gr_363.gif]


[Graphics:../Images/ComplexFunTrigModHome_gr_364.gif]

[Graphics:../Images/ComplexFunTrigModHome_gr_365.gif]


[Graphics:../Images/ComplexFunTrigModHome_gr_366.gif]

[Graphics:../Images/ComplexFunTrigModHome_gr_367.gif]


[Graphics:../Images/ComplexFunTrigModHome_gr_368.gif]

[Graphics:../Images/ComplexFunTrigModHome_gr_369.gif]

Alternate Solution.  Use identity (5-39)   [Graphics:../Images/ComplexFunTrigModHome_gr_370.gif]   and get  

                    [Graphics:../Images/ComplexFunTrigModHome_gr_371.gif]  

We are really really done.   

                    [Graphics:../Images/ComplexFunTrigModHome_gr_372.gif]          [Graphics:../Images/ComplexFunTrigModHome_gr_373.gif]

                    The point  [Graphics:../Images/ComplexFunTrigModHome_gr_374.gif]  and it's image  [Graphics:../Images/ComplexFunTrigModHome_gr_375.gif].  

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexFunTrigModHome_gr_376.gif]

[Graphics:../Images/ComplexFunTrigModHome_gr_377.gif]


[Graphics:../Images/ComplexFunTrigModHome_gr_378.gif]

[Graphics:../Images/ComplexFunTrigModHome_gr_379.gif]

Remark.  

                    [Graphics:../Images/ComplexFunTrigModHome_gr_380.gif]  

 

















 

This solution is complements of the authors.

 



































 

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