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  "body": "\n## Statement\n\nThe [[complex exponential|054VXHMCA3]] $\\exp : \\mathbb{C} \\to \\mathbb{C}$ is an [[entire function|0419794R0T]]: it is complex differentiable at each $z \\in \\mathbb{C}$.\n\n## Remarks\n\nProof: $\\exp$ is given by a power series with infinite radius of convergence, and [[power series are holomorphic in their disc of convergence|0YMP521ZR5]].\nIts [[derivative|019H1Z6419]] is $\\exp$ itself.\n\n## Explanations\n\n### L1 human\n\nThe exponential function has a complex derivative at every point of the plane.\nSo it is a holomorphic function without any exceptional points.\n",
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