9 (c).  Let  [Graphics:Images/ComplexPowerSeriesModHome_gr_665.gif]  and  [Graphics:Images/ComplexPowerSeriesModHome_gr_666.gif]  in part (a) to establish inequality  (4-17).  

Solution 9 (c).

See text and/or instructor's solution manual.

Solution.  From part (a) we have:

[Graphics:../Images/ComplexPowerSeriesModHome_gr_667.gif]

Observe that [Graphics:../Images/ComplexPowerSeriesModHome_gr_668.gif].

Using the inequalities   [Graphics:../Images/ComplexPowerSeriesModHome_gr_669.gif]  and  [Graphics:../Images/ComplexPowerSeriesModHome_gr_670.gif].  in part (b) this implies that

                    [Graphics:../Images/ComplexPowerSeriesModHome_gr_671.gif]   for   [Graphics:../Images/ComplexPowerSeriesModHome_gr_672.gif].

Thus   [Graphics:../Images/ComplexPowerSeriesModHome_gr_673.gif].  

Using this inequality we get inequality  (4-17):

                    [Graphics:../Images/ComplexPowerSeriesModHome_gr_674.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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