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 (c).  [Graphics:Images/ComplexFunExponentialModHome_gr_90.gif].

Solution 4 (c).

See text and/or instructor's solution manual.

Answer.   [Graphics:../Images/ComplexFunExponentialModHome_gr_91.gif].

Solution.    

                     [Graphics:../Images/ComplexFunExponentialModHome_gr_92.gif]  

We are done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexFunExponentialModHome_gr_93.gif]

[Graphics:../Images/ComplexFunExponentialModHome_gr_94.gif]


[Graphics:../Images/ComplexFunExponentialModHome_gr_95.gif]

[Graphics:../Images/ComplexFunExponentialModHome_gr_96.gif]

                    [Graphics:../Images/ComplexFunExponentialModHome_gr_97.gif]          [Graphics:../Images/ComplexFunExponentialModHome_gr_98.gif]

                                        The point  [Graphics:../Images/ComplexFunExponentialModHome_gr_99.gif]  and it's image  [Graphics:../Images/ComplexFunExponentialModHome_gr_100.gif].   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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