Example 5.8.  The values of of  [Graphics:Images/ComplexFunComplexPowerMod_gr_108.gif]  are  

            [Graphics:Images/ComplexFunComplexPowerMod_gr_109.gif]  

where n is an integer.  The principal value of  [Graphics:Images/ComplexFunComplexPowerMod_gr_110.gif]  is  

            [Graphics:Images/ComplexFunComplexPowerMod_gr_111.gif]  

Explore Solution 5.8.

(a) Enter  [Graphics:../Images/ComplexFunComplexPowerMod_gr_113.gif]  and find the principal value.  

[Graphics:../Images/ComplexFunComplexPowerMod_gr_114.gif]

[Graphics:../Images/ComplexFunComplexPowerMod_gr_115.gif]

 

 


(b) Enter  [Graphics:../Images/ComplexFunComplexPowerMod_gr_116.gif]  and find some of its values.  

[Graphics:../Images/ComplexFunComplexPowerMod_gr_117.gif]

[Graphics:../Images/ComplexFunComplexPowerMod_gr_118.gif]

[Graphics:../Images/ComplexFunComplexPowerMod_gr_119.gif]

[Graphics:../Images/ComplexFunComplexPowerMod_gr_120.gif]

 

 

[Graphics:../Images/ComplexFunComplexPowerMod_gr_121.gif]

[Graphics:../Images/ComplexFunComplexPowerMod_gr_122.gif]

[Graphics:../Images/ComplexFunComplexPowerMod_gr_123.gif]

[Graphics:../Images/ComplexFunComplexPowerMod_gr_124.gif]

 

 

Use Mathematica to plot some of the values of  [Graphics:../Images/ComplexFunComplexPowerMod_gr_125.gif].  

[Graphics:../Images/ComplexFunComplexPowerMod_gr_126.gif]

[Graphics:../Images/ComplexFunComplexPowerMod_gr_127.gif]

[Graphics:../Images/ComplexFunComplexPowerMod_gr_128.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell