Thank you for using the site. I'll be happy to help you with this.
I've seen this problem several times, and the mapping function that I have used is:
φ(n) = cos(2n*pi/5) + i * sin(2n*pi/5)
This function will map the values in Z5 to the group of fifth roots that you got from DeMoivre's formula.
A list of the calculated values of φ(n) for all n in Z5 (that is, n = 0, 1, 2, 3, 4) will show that φ(n) is both one-to-one and onto.
Let me know if you need more than this. I can send the complete solution for this part if you need it.
No problem. Here is the complete solution for both parts of this problem:
Please let me know if you have any additional questions about this.