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  "body": "\n## Proof\n\n1. The [[imaginary unit|0ESCX36MMC]] is the complex number $i = 0 + 1 i$, with real part $0$ and imaginary part $1$.\n2. The product of [[complex numbers|09FTAET5Z4]] is $(a + b i)(c + d i) = (a c - b d) + (a d + b c) i$.\n3. Take $a = c = 0$ and $b = d = 1$. Then $i^2 = (0 \\cdot 0 - 1 \\cdot 1) + (0 \\cdot 1 + 1 \\cdot 0) i = -1 + 0 i$.\n4. The complex number $-1 + 0 i$ is the real number $-1$, since $\\R$ sits in $\\C$ as the numbers $a + 0 i$. So $i^2 = -1$.\n\n## Idea\n\nThe rule for multiplying complex numbers is built so that the two imaginary parts multiply to a negative real number. For $i \\cdot i$ this gives exactly $-1$.\n",
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  "name": "Proof that i squared is minus one",
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