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  "body": "\n## Statement\n\nLet $n$ be a positive integer.\nThen there are exactly $n$ complex $n$th [[roots of unity|0S61N75H45]].\n\n## Remarks\n\nThe [[list of the nth roots of unity|057BH3JC9S]] has $n$ numbers $e^{2 \\pi i k / n}$ with $0 \\le k \u003c n$.\nThey are pairwise different, because their arguments are different numbers in $[0, 2\\pi)$.\nA polynomial of degree $n$ has at most $n$ roots in a field, so $X^n - 1$ has no other roots.\nIn other fields there can be fewer: in $\\mathbb{R}$, the only $4$th roots of unity are $1$ and $-1$.\n\n## Explanations\n\n### L1 human\n\nThe equation $z^n = 1$ has exactly $n$ complex solutions.\nOver the real numbers, it has only one or two solutions, so most of the solutions are not real.\n",
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