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  "body": "\n## Definition\n\nA complex number $\\alpha$ is algebraic if there is a nonzero polynomial $f$ with rational coefficients such that $f(\\alpha) = 0$.\nThe degree of $\\alpha$ is the smallest degree of such a polynomial.\n\n## Remarks\n\nOne may use integer coefficients instead, by clearing denominators.\nExamples are each rational number (degree $1$), $\\sqrt{2}$ and $i$ (degree $2$), and $\\sqrt[3]{2}$ (degree $3$).\nThe algebraic numbers form a field, and this field is countable.\nA complex number that is not algebraic is [[transcendental|079EGSD32Y]].\n\n## Explanations\n\n### L1 human\n\nAn algebraic number is a solution of a polynomial equation with integer coefficients.\nFor example, $\\sqrt{2}$ is algebraic because it solves $x^2 - 2 = 0$.\n",
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