On the edge of completing this proof about the order of an element

jdinatale
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Homework Statement


finish.jpg



The Attempt at a Solution



Based on my attempt above, I have demonstrated that the order is less than or equal to n. I am certain that it is actually n, but I'm not sure which theorem I can grab finish this thing off. Any tips for pointing me in the right direction?
 
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(bab^(-1))^m is equal to b*a^m*b^(-1) for any m. You've shown that. If that's equal to e for m<n, then was the order of a really n?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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