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  "body": "\n## Definition\n\nLet $z$ be a [[complex number|09FTAET5Z4]] with $z \\neq 0$, and let $|z|$ be its [[modulus|0KW2X0TFBX]].\nAn argument of $z$ is a real number $\\theta$ with\n$$z = |z| (\\cos \\theta + i \\sin \\theta).$$\nThe notation $\\arg z$ means the set of all arguments of $z$, or one chosen argument.\n\n## Remarks\n\nIf $\\theta$ is an argument of $z$, then the arguments of $z$ are exactly the numbers $\\theta + 2 \\pi k$ with $k \\in \\mathbb{Z}$.\nThe number $0$ has no argument in this sense. Some conventions set $\\arg 0 = 0$.\nFor example, the arguments of $i$ are $\\pi/2 + 2 \\pi k$, and those of $-1$ are $\\pi + 2 \\pi k$.\n\n## Explanations\n\n### L1 human\n\nThe argument says in which direction a complex number points from $0$.\nThe number $1 + i$ points at $45$ degrees, so $\\pi/4$ is an argument of it.\nA full turn brings you back to the same direction, so adding $2\\pi$ gives another argument.\n",
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