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  "body": "\n## Statement\n\nLet $n$ be a positive integer.\nThen $e^{2 \\pi i / n}$ is a [[primitive root of unity|0J817RTVG6]].\n\n## Remarks\n\nProof: for $1 \\le k \u003c n$, the number $\\zeta^k = e^{2 \\pi i k / n}$ has argument $2 \\pi k / n$, which is strictly between $0$ and $2\\pi$. Thus $\\zeta^k \\neq 1$.\nFor $n = 4$ this number is $i$, and for $n = 2$ it is $-1$.\n\n## Explanations\n\n### L1 human\n\nThe first root of unity after $1$, going counterclockwise around the circle, is a primitive one.\nIts powers walk around the circle step by step and visit every $n$th root of unity before they return to $1$.\n",
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