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  "body": "\n## Description\n\nThe imaginary unit is the [[complex number|09FTAET5Z4]] $i = 0 + 1 i$. It satisfies $i^2 = -1$, see [[i squared is minus one|07KBQCG9KV]].\nIt is a solution of the equation $x^2 + 1 = 0$. The other solution is $-i$.\nIn the [[complex plane|0CTE7A31XQ]], $i$ is the point $(0, 1)$, at distance $1$ above $0$.\n\n## Remarks\n\nThe powers of $i$ repeat with period $4$: $i^0 = 1$, $i^1 = i$, $i^2 = -1$, $i^3 = -i$ and $i^4 = 1$.\nMultiplication by $i$ turns the complex plane by a quarter turn about $0$, counterclockwise.\nIn electrical engineering, people often write $j$ for $i$.\n\n## Explanations\n\n### L1 human\n\nThe imaginary unit is a new number whose square is $-1$.\nNo real number has this property, so $i$ is not on the real number line.\nIt sits one unit above $0$ in the plane of complex numbers.\n",
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