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Homework Statement
Show that primitive n-th roots of unity have the form [itex]e^{i2\pi k/n}[/itex] for [itex]k\in\mathbb{Z},n\in\mathbb{N}[/itex], [itex]k[/itex] and [itex]n[/itex] coprime.
The attempt at a solution
So the n-th roots of unity [itex]z[/itex] have the property [itex]z^{n}=1[/itex]. I have previously shown that [itex](e^{2\pi ik/n})^{n}=e^{2\pi ik}=(e^{2\pi i})^{k}=1^{k}=1 [/itex]. However, I'm not sure where to start in proving that primitive n-th roots of unity have that property. Any ideas on where I could get started?