"de Moivre's formula" meaning in English

{
  "etymology_text": "Named after Abraham de Moivre (1667–1754), French mathematician.",
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      "glosses": [
        "A formula that connects trigonometry and complex numbers, stating that, for any complex number (and, in particular, for any real number) x and integer n, big ( cos (x)+i sin (x) big )ⁿ= cos (nx)+i sin (nx), where i is the imaginary unit."
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          "mathematics",
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        [
          "trigonometry",
          "trigonometry"
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          "complex number",
          "complex number"
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          "real number",
          "real number"
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          "integer",
          "integer"
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          "imaginary unit",
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      "raw_glosses": [
        "(mathematics) A formula that connects trigonometry and complex numbers, stating that, for any complex number (and, in particular, for any real number) x and integer n, big ( cos (x)+i sin (x) big )ⁿ= cos (nx)+i sin (nx), where i is the imaginary unit."
      ],
      "synonyms": [
        {
          "word": "de Moivre's identity"
        },
        {
          "word": "de Moivre's theorem"
        }
      ],
      "topics": [
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Abraham de Moivre"
      ]
    }
  ],
  "word": "de Moivre's formula"
}

{
  "etymology_text": "Named after Abraham de Moivre (1667–1754), French mathematician.",
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      "glosses": [
        "A formula that connects trigonometry and complex numbers, stating that, for any complex number (and, in particular, for any real number) x and integer n, big ( cos (x)+i sin (x) big )ⁿ= cos (nx)+i sin (nx), where i is the imaginary unit."
      ],
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        [
          "mathematics",
          "mathematics"
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        [
          "trigonometry",
          "trigonometry"
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          "complex number",
          "complex number"
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          "real number",
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        "(mathematics) A formula that connects trigonometry and complex numbers, stating that, for any complex number (and, in particular, for any real number) x and integer n, big ( cos (x)+i sin (x) big )ⁿ= cos (nx)+i sin (nx), where i is the imaginary unit."
      ],
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  "synonyms": [
    {
      "word": "de Moivre's identity"
    },
    {
      "word": "de Moivre's theorem"
    }
  ],
  "word": "de Moivre's formula"
}