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  "body": "\n## Statement\n\nFor each complex number $z$, $|\\bar{z}| = |z|$.\nHere $\\bar{z}$ is the [[complex conjugate|0BJV24C4SY]] of $z$ and $|\\cdot|$ is the [[modulus|0KW2X0TFBX]].\n\n## Remarks\n\nProof: for $z = a + b i$, $|\\bar{z}| = \\sqrt{a^2 + (-b)^2} = \\sqrt{a^2 + b^2} = |z|$.\nIn the complex plane, this says that a reflection in the real axis does not change the distance to $0$.\n\n## Explanations\n\n### L1 human\n\nA number and its conjugate are mirror images in the real axis.\nA mirror keeps distances, so both numbers are at the same distance from $0$.\n",
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