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 (f).  [Graphics:Images/ComplexFunExponentialModHome_gr_119.gif].

Solution 4 (f).

See text and/or instructor's solution manual.

Answer.   [Graphics:../Images/ComplexFunExponentialModHome_gr_120.gif].  

Solution.    

                      

We are done.   

Aside.  We can let Mathematica check our work.

[Graphics:../Images/ComplexFunExponentialModHome_gr_122.gif]


[Graphics:../Images/ComplexFunExponentialModHome_gr_123.gif]

 [Graphics:../Images/ComplexFunExponentialModHome_gr_124.gif]          [Graphics:../Images/ComplexFunExponentialModHome_gr_125.gif]

                                        The point  [Graphics:../Images/ComplexFunExponentialModHome_gr_126.gif]  and it's image  [Graphics:../Images/ComplexFunExponentialModHome_gr_127.gif].  

We are really done.   

Aside.  Look what happens if we switch the real and imaginary parts.

Contrast the above solution with  [Graphics:../Images/ComplexFunExponentialModHome_gr_128.gif],  which is obviously different.

                    [Graphics:../Images/ComplexFunExponentialModHome_gr_129.gif]  

 

We are really really done.   

Aside.  We can let Mathematica double check our work.

 

[Graphics:../Images/ComplexFunExponentialModHome_gr_130.gif]

[Graphics:../Images/ComplexFunExponentialModHome_gr_131.gif]

                    [Graphics:../Images/ComplexFunExponentialModHome_gr_132.gif]          [Graphics:../Images/ComplexFunExponentialModHome_gr_133.gif]

                                                            The point  [Graphics:../Images/ComplexFunExponentialModHome_gr_134.gif]  and it's image  [Graphics:../Images/ComplexFunExponentialModHome_gr_135.gif].  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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