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## Homework Statement

I must show that cos(2pi/n) + isin(2pi/n) is a primitive root of unity

## Homework Equations

a primitive root of unity is an nth root of unity that does not equal 1 when raised to the kth power for k less than n and great than or equal to 1

## The Attempt at a Solution

If we set z = cos(2pi/n) + isin(2pi/n) then z^k cannot equal 1. we can use de moivres theorem to make z^k = cos(2kpi/n) + isin(2kpi/n) and then I'm not certain what fact to use next