Exercise 3.  Show that, if  [Graphics:Images/ComplexFunComplexPowerModHome_gr_184.gif],  then  [Graphics:Images/ComplexFunComplexPowerModHome_gr_185.gif]  has a unique value.

Solution 3.

See text and/or instructor's solution manual.

Solution.   All the values for  [Graphics:../Images/ComplexFunComplexPowerModHome_gr_186.gif]  are  [Graphics:../Images/ComplexFunComplexPowerModHome_gr_187.gif].  

Recall that  [Graphics:../Images/ComplexFunComplexPowerModHome_gr_188.gif]  which collapses to the single element zero, i.e.   [Graphics:../Images/ComplexFunComplexPowerModHome_gr_189.gif].  

Therefore, for  [Graphics:../Images/ComplexFunComplexPowerModHome_gr_190.gif],   we have   [Graphics:../Images/ComplexFunComplexPowerModHome_gr_191.gif].

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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