"imaginary unit" meaning in English

See imaginary unit in All languages combined, or Wiktionary

Noun

Forms: imaginary units [plural]
Etymology: So named because it takes on the role of unit for the imaginary part of a complex number. Head templates: {{en-noun}} imaginary unit (plural imaginary units)
  1. (number theory, complex analysis, quaternion theory) An imaginary number (in the case of complex numbers, usually denoted i) that is defined as a solution to the equation x²=-1. Wikipedia link: imaginary unit Categories (topical): Complex analysis, Number theory Translations (imaginary number): imaginaariyksikkö (Finnish), unité imaginaire [feminine] (French), imaginäre Einheit [feminine] (German), अधिकल्पित एकक (adhikalpit ekak) [masculine] (Hindi), unità immaginaria [feminine] (Italian), 虚数単位 (kyosū tan'i) (Japanese), 허수단위 (heosudanwi) (Korean), unitas imaginaria [feminine] (Latin), jednostka urojona [feminine] (Polish), мни́мая едини́ца (mnímaja jediníca) [feminine] (Russian), หน่วยจินตภาพ (nùai-jin-dtà-pâap) (Thai)

Inflected forms

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          "text": "In Section 4.3 we introduced the imaginary unit i with (i)²#61;-1, in the complex space domain. In section 4.4 we introduced the complex unit j with (j)²#61;-1, in connection with the time dependency of the shape (4.4.16) of the swimming profile. These different imaginary units have no interaction, we leave unaltered the product ij.",
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          "text": "2014, Dennis G. Zill, Warren S. Wright, Advanced Engineering Mathematics, Ascend Learning (Jones & Bartlett Learning), 5th Edition, page 793,\nWe now simply say that i is the imaginary unit and define it by the property i²=-1. Using the imaginary unit, we build a general complex number out of two real numbers."
        },
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          "ref": "2021, Bruce Hunt, Locally Mixed Symmetric Spaces, Springer, page 123:",
          "text": "Consider now in addition to the given #92;H#92;subset#92;mathbb#123;O#125;, one of the totally imaginary units not contained in #92;H, and note that #123;SU#125;(2) acts transitively on the set of totally imaginary units of a quaternion algebra; as we are assuming #92;alpha#92;notin#92;H, we may in fact assume that #92;mathbb#123;O#125;#61;#92;H#92;oplus#92;H' with #92;alpha#92;in#92;H'.",
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        "An imaginary number (in the case of complex numbers, usually denoted i) that is defined as a solution to the equation x²=-1."
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          "code": "fi",
          "lang": "Finnish",
          "sense": "imaginary number",
          "word": "imaginaariyksikkö"
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          "code": "fr",
          "lang": "French",
          "sense": "imaginary number",
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          "code": "de",
          "lang": "German",
          "sense": "imaginary number",
          "tags": [
            "feminine"
          ],
          "word": "imaginäre Einheit"
        },
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          "lang": "Hindi",
          "roman": "adhikalpit ekak",
          "sense": "imaginary number",
          "tags": [
            "masculine"
          ],
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        },
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            "feminine"
          ],
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        },
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          "sense": "imaginary number",
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        },
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          "lang": "Korean",
          "roman": "heosudanwi",
          "sense": "imaginary number",
          "word": "허수단위"
        },
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          "lang": "Latin",
          "sense": "imaginary number",
          "tags": [
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          ],
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        },
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          "sense": "imaginary number",
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        },
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          "code": "ru",
          "lang": "Russian",
          "roman": "mnímaja jediníca",
          "sense": "imaginary number",
          "tags": [
            "feminine"
          ],
          "word": "мни́мая едини́ца"
        },
        {
          "code": "th",
          "lang": "Thai",
          "roman": "nùai-jin-dtà-pâap",
          "sense": "imaginary number",
          "word": "หน่วยจินตภาพ"
        }
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      "code": "fi",
      "lang": "Finnish",
      "sense": "imaginary number",
      "word": "imaginaariyksikkö"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "imaginary number",
      "tags": [
        "feminine"
      ],
      "word": "unité imaginaire"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "imaginary number",
      "tags": [
        "feminine"
      ],
      "word": "imaginäre Einheit"
    },
    {
      "code": "hi",
      "lang": "Hindi",
      "roman": "adhikalpit ekak",
      "sense": "imaginary number",
      "tags": [
        "masculine"
      ],
      "word": "अधिकल्पित एकक"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "imaginary number",
      "tags": [
        "feminine"
      ],
      "word": "unità immaginaria"
    },
    {
      "code": "ja",
      "lang": "Japanese",
      "roman": "kyosū tan'i",
      "sense": "imaginary number",
      "word": "虚数単位"
    },
    {
      "code": "ko",
      "lang": "Korean",
      "roman": "heosudanwi",
      "sense": "imaginary number",
      "word": "허수단위"
    },
    {
      "code": "la",
      "lang": "Latin",
      "sense": "imaginary number",
      "tags": [
        "feminine"
      ],
      "word": "unitas imaginaria"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "imaginary number",
      "tags": [
        "feminine"
      ],
      "word": "jednostka urojona"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "mnímaja jediníca",
      "sense": "imaginary number",
      "tags": [
        "feminine"
      ],
      "word": "мни́мая едини́ца"
    },
    {
      "code": "th",
      "lang": "Thai",
      "roman": "nùai-jin-dtà-pâap",
      "sense": "imaginary number",
      "word": "หน่วยจินตภาพ"
    }
  ],
  "word": "imaginary unit"
}

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