Homomorphism of groups question

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*edit* problem solved.
 
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Here is a hint: let's say you have some element g that maps to some nonzero integer m. What does gn map to? Is there something wrong that inevitably happens?
 
Awesome that helped a lot.
 
Unfortunately, since you went back and erased the original question, others, who might have similar questions, cannot learn from this. Please do NOT erase the original questions just because you do not need them any more.
 
Why on Earth would you erase the question? The point of a forum is that you can have discussions and read/refer to them back.
 

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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