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  "body": "\n## Definition\n\nLet $z = a + b i$ be a [[complex number|09FTAET5Z4]], with $a$ and $b$ real.\nThe complex conjugate of $z$ is the complex number $\\bar{z} = a - b i$.\n\n## Remarks\n\nAnother common notation is $z^*$.\nConjugation respects the operations: $\\overline{z + w} = \\bar{z} + \\bar{w}$ and $\\overline{z w} = \\bar{z} \\, \\bar{w}$. Also $\\bar{\\bar{z}} = z$.\nA complex number $z$ is real exactly when $\\bar{z} = z$.\nThe product $z \\bar{z}$ is the real number $|z|^2$, see [[a complex number times its conjugate|0ZB7J071WQ]].\n\n## Explanations\n\n### L1 human\n\nTo conjugate a complex number, change the sign of its imaginary part.\nFor example, the conjugate of $2 + 5 i$ is $2 - 5 i$, and the conjugate of $7$ is $7$.\n",
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