Exercise 4.  Express  [Graphics:Images/ComplexFunExponentialModHome_gr_61.gif]  in the form  [Graphics:Images/ComplexFunExponentialModHome_gr_62.gif]  for the following values of  z.  

4 (a).  [Graphics:Images/ComplexFunExponentialModHome_gr_63.gif].

Solution 4 (a).

See text and/or instructor's solution manual.

Answer   [Graphics:../Images/ComplexFunExponentialModHome_gr_64.gif]

Solution.    

                    [Graphics:../Images/ComplexFunExponentialModHome_gr_65.gif]  

We are done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexFunExponentialModHome_gr_66.gif]

[Graphics:../Images/ComplexFunExponentialModHome_gr_67.gif]

                    [Graphics:../Images/ComplexFunExponentialModHome_gr_68.gif]          [Graphics:../Images/ComplexFunExponentialModHome_gr_69.gif]

                                                  The point  [Graphics:../Images/ComplexFunExponentialModHome_gr_70.gif]  and it's image  [Graphics:../Images/ComplexFunExponentialModHome_gr_71.gif].  

We are really done.   

Aside.  Look what happens if we switch the real and imaginary parts, i.e. from  [Graphics:../Images/ComplexFunExponentialModHome_gr_72.gif]  to  [Graphics:../Images/ComplexFunExponentialModHome_gr_73.gif].

Contrast the above solution with the one using  [Graphics:../Images/ComplexFunExponentialModHome_gr_74.gif],  which is obviously different.

[Graphics:../Images/ComplexFunExponentialModHome_gr_75.gif][Graphics:../Images/ComplexFunExponentialModHome_gr_76.gif].  

                    [Graphics:../Images/ComplexFunExponentialModHome_gr_77.gif]          [Graphics:../Images/ComplexFunExponentialModHome_gr_78.gif]

                                                            The point  [Graphics:../Images/ComplexFunExponentialModHome_gr_79.gif]  and it's image  [Graphics:../Images/ComplexFunExponentialModHome_gr_80.gif].   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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