Exercise 11.  Let   [Graphics:Images/ComplexSequenceSeriesModHome_gr_298.gif].  

If  [Graphics:Images/ComplexSequenceSeriesModHome_gr_299.gif]  is a complex constant, show that   [Graphics:Images/ComplexSequenceSeriesModHome_gr_300.gif].  

Solution 11.

See text and/or instructor's solution manual.

Solution.   By Theorem 4.4,   [Graphics:../Images/ComplexSequenceSeriesModHome_gr_301.gif],   and   [Graphics:../Images/ComplexSequenceSeriesModHome_gr_302.gif],   and   [Graphics:../Images/ComplexSequenceSeriesModHome_gr_303.gif].  

Another application of  Theorem 4.4 can be used to obtain:  

                    [Graphics:../Images/ComplexSequenceSeriesModHome_gr_304.gif]  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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