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  "body": "\n## Definition\n\nLet $n$ be a positive integer.\nA complex number $z$ is an $n$th root of unity when $z^n = 1$.\nA complex number $z$ is a root of unity when it is an $n$th root of unity for some positive integer $n$.\n\n## Remarks\n\nThe same definition works in any field, or in any commutative ring.\nThe $n$th roots of unity in $\\mathbb{C}$ form a group under multiplication, written $\\mu_n$.\nFor example, the $4$th roots of unity are $1$, $i$, $-1$ and $-i$.\nEach root of unity $z$ satisfies $|z| = 1$, because $|z|^n = |z^n| = 1$.\n\n## Explanations\n\n### L1 human\n\nA root of unity is a number that gives $1$ when you multiply it by itself often enough.\nThe number $-1$ is one, because $(-1)^2 = 1$, and so is $i$, because $i^4 = 1$.\n",
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