Exercise 7.  Does 1 raised to any power always equal 1?   Why or why not?  

Solution 7.

See text and/or instructor's solution manual.

Solution.   No.  Calculation reveals that  

                    [Graphics:../Images/ComplexFunComplexPowerModHome_gr_234.gif]  

where n is an integer.

We are done.   

Aside.  We can let Mathematica double check our work.

[Graphics:../Images/ComplexFunComplexPowerModHome_gr_235.gif]

[Graphics:../Images/ComplexFunComplexPowerModHome_gr_236.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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