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  "body": "\n## Summary\n\nThe complex plane is the plane $\\mathbb{R}^2$ in which the point $(a, b)$ represents the [[complex number|09FTAET5Z4]] $a + b i$.\nThe horizontal axis is the real axis and the vertical axis is the imaginary axis.\nIn this picture, addition of complex numbers is addition of vectors.\nThe [[modulus|0KW2X0TFBX]] $|z|$ is the distance from $z$ to $0$, and the [[argument|0ZZRSX91QR]] of $z$ is the angle from the positive real axis to $z$.\n\n## Remarks\n\nMultiplication by a complex number $w \\neq 0$ scales the plane by $|w|$ and turns it by the argument of $w$.\nThe [[complex conjugate|0BJV24C4SY]] is the reflection in the real axis.\n\n## Explanations\n\n### L1 human\n\nDraw the real numbers on a horizontal line, and draw the multiples of $i$ on a vertical line through $0$.\nThen each complex number is a point of the plane: $3 + 2 i$ is three steps to the right and two steps up.\n",
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