What is the Finite Field Order of Z[i]/A in Z[i] with A=<1+i>?

missavvy
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Homework Statement



If A=<1+i> in Z, show that Z/A is a finite field and find its order

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The Attempt at a Solution



Not sure where to start...

Z/A = {m+ni + A, m, n integers} ? is that right?

And I don't know what else to do.
 
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Maybe you can use that 2=(1+i)(1-i)...
 

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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