What are the elements of each order in D_n+Z_9 for n = 7 and 11?

ccrfan44
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Pick a number n which is the product of 2 distinct primes 5 or more. Find the number of elements of each order in the groupd D(sub)n+Z(sub)9, completely explaining your work. Verify that these number add up to the order of the group.

Ive used 7 and 11 as my primes. So now do I use these primes in D_n since to where i get D_7+Z_9 and D_11+Z_9? This is where I am confused.
 
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Also once i have that info, then where do i go from here?
 

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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