9 (b).  Explain why, in Inequality (4-17) ,   [Graphics:Images/ComplexPowerSeriesModHome_gr_653.gif]  and  [Graphics:Images/ComplexPowerSeriesModHome_gr_654.gif].  

Solution 9 (b).

See text and/or instructor's solution manual.

Solution.  As mentioned in the proof:  Let  [Graphics:../Images/ComplexPowerSeriesModHome_gr_655.gif].  Choose  [Graphics:../Images/ComplexPowerSeriesModHome_gr_656.gif]  so that  [Graphics:../Images/ComplexPowerSeriesModHome_gr_657.gif].  

Since  [Graphics:../Images/ComplexPowerSeriesModHome_gr_658.gif]  we see that   [Graphics:../Images/ComplexPowerSeriesModHome_gr_659.gif].

As mentioned in the proof:  Choose  [Graphics:../Images/ComplexPowerSeriesModHome_gr_660.gif]  to be small enough so that  [Graphics:../Images/ComplexPowerSeriesModHome_gr_661.gif].

Since  [Graphics:../Images/ComplexPowerSeriesModHome_gr_662.gif]  and  [Graphics:../Images/ComplexPowerSeriesModHome_gr_663.gif]  we see that   [Graphics:../Images/ComplexPowerSeriesModHome_gr_664.gif].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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