"complex conjugate root theorem" meaning in All languages combined

See complex conjugate root theorem on Wiktionary

Proper name [English]

Head templates: {{en-proper-noun}} complex conjugate root theorem
  1. (mathematics, complex analysis) The theorem that if a complex number is a root for a polynomial with real coefficients, the complex conjugate of that number will also be a root. Wikipedia link: complex conjugate root theorem Categories (topical): Complex analysis, Mathematics
    Sense id: en-complex_conjugate_root_theorem-en-name-st8bFrIR Categories (other): English entries with incorrect language header, Pages with 1 entry, Pages with entries Topics: complex-analysis, mathematics, sciences
{
  "head_templates": [
    {
      "args": {},
      "expansion": "complex conjugate root theorem",
      "name": "en-proper-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Complex analysis",
          "orig": "en:Complex analysis",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "The theorem that if a complex number is a root for a polynomial with real coefficients, the complex conjugate of that number will also be a root."
      ],
      "id": "en-complex_conjugate_root_theorem-en-name-st8bFrIR",
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "complex analysis",
          "complex analysis"
        ],
        [
          "theorem",
          "theorem"
        ],
        [
          "complex number",
          "complex number"
        ],
        [
          "root",
          "root"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "real",
          "real"
        ],
        [
          "coefficient",
          "coefficient"
        ],
        [
          "complex conjugate",
          "complex conjugate"
        ]
      ],
      "raw_glosses": [
        "(mathematics, complex analysis) The theorem that if a complex number is a root for a polynomial with real coefficients, the complex conjugate of that number will also be a root."
      ],
      "topics": [
        "complex-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "complex conjugate root theorem"
      ]
    }
  ],
  "word": "complex conjugate root theorem"
}
{
  "head_templates": [
    {
      "args": {},
      "expansion": "complex conjugate root theorem",
      "name": "en-proper-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "name",
  "senses": [
    {
      "categories": [
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English proper nouns",
        "English uncountable nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Complex analysis",
        "en:Mathematics"
      ],
      "glosses": [
        "The theorem that if a complex number is a root for a polynomial with real coefficients, the complex conjugate of that number will also be a root."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
          "complex analysis",
          "complex analysis"
        ],
        [
          "theorem",
          "theorem"
        ],
        [
          "complex number",
          "complex number"
        ],
        [
          "root",
          "root"
        ],
        [
          "polynomial",
          "polynomial"
        ],
        [
          "real",
          "real"
        ],
        [
          "coefficient",
          "coefficient"
        ],
        [
          "complex conjugate",
          "complex conjugate"
        ]
      ],
      "raw_glosses": [
        "(mathematics, complex analysis) The theorem that if a complex number is a root for a polynomial with real coefficients, the complex conjugate of that number will also be a root."
      ],
      "topics": [
        "complex-analysis",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "complex conjugate root theorem"
      ]
    }
  ],
  "word": "complex conjugate root theorem"
}

Download raw JSONL data for complex conjugate root theorem meaning in All languages combined (1.2kB)


This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-03-01 from the enwiktionary dump dated 2025-02-21 using wiktextract (7c21d10 and f2e72e5). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.