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  "body": "\n## Statement\n\nThe [[complex numbers|09FTAET5Z4]] $\\mathbb{C}$, with their addition and multiplication, form a field.\nThat is, $\\mathbb{C}$ is a commutative ring with $0 \\neq 1$, and each complex number $z \\neq 0$ has a multiplicative inverse $z^{-1}$ with $z z^{-1} = 1$.\n\n## Remarks\n\nThe [[inverse of a complex number|0FQRAV5SKH]] $a + b i \\neq 0$ is $\\dfrac{a - b i}{a^2 + b^2}$.\nThe field $\\mathbb{C}$ contains $\\mathbb{R}$ as a subfield. It has dimension $2$ as a vector space over $\\mathbb{R}$, with basis $1, i$.\nThe field $\\mathbb{C}$ is algebraically closed, but it is not an ordered field.\n\n## Explanations\n\n### L1 human\n\nYou can add, subtract, multiply and divide complex numbers, as with real numbers.\nThe only exception is division by $0$.\nFor example, $\\dfrac{1}{i} = -i$, because $i \\cdot (-i) = -i^2 = 1$.\n",
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