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  "body": "\n## Summary\n\nA complex logarithm of a nonzero complex number $z$ is a complex number $w$ with $e^w = z$, see the [[definition|0X2FY491PF]].\nEach $z \\neq 0$ has infinitely many logarithms, which differ by integer multiples of $2\\pi i$.\nA complex logarithm function is a continuous choice of a logarithm on an open subset of $\\mathbb{C} \\setminus \\{0\\}$.\n",
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