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  "body": "\n## Definition\n\nLet $z$ be a [[complex number|09FTAET5Z4]] with real part $a = \\operatorname{Re} z$ and imaginary part $b = \\operatorname{Im} z$.\nThe modulus, or absolute value, of $z$ is the nonnegative real number\n$$|z| = \\sqrt{a^2 + b^2}.$$\n\n## Remarks\n\nFor a real number $z = a$, the modulus is $\\sqrt{a^2} = |a|$, the [[absolute value|00S7C68D51]] of $a$.\nIn the [[complex plane|0CTE7A31XQ]], $|z|$ is the distance from $z$ to $0$, by the Pythagorean theorem. The distance between $z$ and $w$ is $|z - w|$.\nFor example, $|3 + 4 i| = 5$.\n\n## Explanations\n\n### L1 human\n\nThe modulus of a complex number is its length, that is, its distance from $0$ in the plane.\nThe point $3 + 4 i$ is the corner of a right triangle with sides $3$ and $4$, so its distance from $0$ is $5$.\n",
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