Solution 7.

See text and/or instructor's solution manual.

Answer.   This follows immediately from Property (5-4)  [Graphics:../Images/ComplexFunExponentialModHome_gr_290.gif],  if and only if  [Graphics:../Images/ComplexFunExponentialModHome_gr_291.gif],  for some integer  n.

Solution.   

                    [Graphics:../Images/ComplexFunExponentialModHome_gr_292.gif]

We are done.   

Remark.  Indeed, there is an relation     [Graphics:../Images/ComplexFunExponentialModHome_gr_293.gif].

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexFunExponentialModHome_gr_294.gif]

[Graphics:../Images/ComplexFunExponentialModHome_gr_295.gif]


[Graphics:../Images/ComplexFunExponentialModHome_gr_296.gif]

[Graphics:../Images/ComplexFunExponentialModHome_gr_297.gif]


[Graphics:../Images/ComplexFunExponentialModHome_gr_298.gif]

[Graphics:../Images/ComplexFunExponentialModHome_gr_299.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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