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  "body": "\n## Statement\n\nLet $z$ be a complex number and let $n$ be a positive integer.\nThen there is a complex number $w$ with $w^n = z$.\n\n## Remarks\n\nFor $z = r e^{i \\theta}$ with $r \u003e 0$, one solution is $w = r^{1/n} e^{i \\theta / n}$, by the [[polar form|0BRXFNQ5JV]].\nFor $z \\neq 0$, there are exactly $n$ solutions. They are $w$ times the $n$th [[roots of unity|0E021GF2B8]].\nThis fact is a special case of the fundamental theorem of algebra.\n\n## Explanations\n\n### L1 human\n\nEvery complex number has a square root, a cube root, and so on.\nFor example, $-1$ has the square roots $i$ and $-i$, and $i$ has the square roots $\\pm \\frac{\\sqrt{2}}{2}(1 + i)$.\nTo take an $n$th root, take the $n$th root of the length and divide the angle by $n$.\n",
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