Exercise 13.  Let  [Graphics:Images/ComplexAlgebraRevisitedModHome_gr_368.gif]  be an nth root of unity.  Prove that  [Graphics:Images/ComplexAlgebraRevisitedModHome_gr_369.gif].    

Solution 13.

See text and/or instructor's solution manual.

Use exercise 11 (a) and recall that if   [Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_370.gif]  is an [Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_371.gif] root of unity, then   [Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_372.gif].   For [Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_373.gif],

        [Graphics:../Images/ComplexAlgebraRevisitedModHome_gr_374.gif]  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

This solution is complements of the authors.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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