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  "body": "\n## Statement\n\nLet $z$ and $w$ be complex numbers.\nThen $z = w$ if and only if $\\operatorname{Re} z = \\operatorname{Re} w$ and $\\operatorname{Im} z = \\operatorname{Im} w$.\n\n## Remarks\n\nHere $\\operatorname{Re}$ and $\\operatorname{Im}$ are the [[real and imaginary parts|02ZE6JHJ7G]].\nThus one equation between complex numbers gives two equations between real numbers.\nFor example, $x + y i = 3 - 2 i$ with $x, y$ real means $x = 3$ and $y = -2$.\n\n## Explanations\n\n### L1 human\n\nTwo complex numbers are equal when their real parts agree and their imaginary parts agree.\nIn the plane, this says that two points are equal when both of their coordinates agree.\n",
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