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  "body": "\n## Summary\n\nThe zeros of a [[meromorphic function|0ZZ7ZYDR8W]] are the points where it takes the value $0$.\nIts poles are the points where it tends to $\\infty$.\nSee the [[definition|9DNDF7AX59]].\nThey are the two kinds of special points of a meromorphic function, and they are exchanged by $f \\mapsto 1/f$.\nCounting them, each with its [[order|23ASRP0MWR]], is the subject of the [[argument principle|0PN2BXRS8G]] and of [[Rouché's theorem|0D430QR02W]].\n\n## Explanations\n\n### L1 human\n\nPicture the graph of $\\abs{f}$ over the complex plane as a landscape.\nThe zeros are the points where the landscape touches the ground.\nThe poles are the points where it shoots up to infinity, like tent poles holding up a tent.\nFor a rational function such as $(z - 1)/(z^2 + 1)$, the zeros are the roots of the numerator and the poles are the roots of the denominator.\n",
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