See imaginary unit on Wiktionary
Download JSON data for imaginary unit meaning in All languages combined (4.5kB)
{
"etymology_text": "So named because it takes on the role of unit for the imaginary part of a complex number.",
"forms": [
{
"form": "imaginary units",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "imaginary unit (plural imaginary units)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Japanese terms with redundant script codes",
"parents": [
"Terms with redundant script codes",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Korean terms with redundant script codes",
"parents": [
"Terms with redundant script codes",
"Entry maintenance"
],
"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": "Number theory",
"orig": "en:Number theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"ref": "2013, J. A. Sparenberg, Hydrodynamic Propulsion and Its Optimization, Springer, page 183",
"text": "In Section 4.3 we introduced the imaginary unit i with (i)²#x3D;-1, in the complex space domain. In section 4.4 we introduced the complex unit j with (j)²#x3D;-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.",
"type": "quotation"
},
{
"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."
},
{
"ref": "2021, Bruce Hunt, Locally Mixed Symmetric Spaces, Springer, page 123",
"text": "Consider now in addition to the given #x5C;H#x5C;subset#x5C;mathbb#x7B;O#x7D;, one of the totally imaginary units not contained in #x5C;H, and note that #x7B;SU#x7D;(2) acts transitively on the set of totally imaginary units of a quaternion algebra; as we are assuming #x5C;alpha#x5C;notin#x5C;H, we may in fact assume that #x5C;mathbb#x7B;O#x7D;#x3D;#x5C;H#x5C;oplus#x5C;H' with #x5C;alpha#x5C;in#x5C;H'.",
"type": "quotation"
}
],
"glosses": [
"An imaginary number (in the case of complex numbers, usually denoted i) that is defined as a solution to the equation x²=-1."
],
"id": "en-imaginary_unit-en-noun-NsZXJ1t8",
"links": [
[
"number theory",
"number theory"
],
[
"complex analysis",
"complex analysis"
],
[
"imaginary number",
"imaginary number"
],
[
"complex number",
"complex number"
],
[
"solution",
"solution"
],
[
"equation",
"equation"
]
],
"qualifier": "quaternion theory",
"raw_glosses": [
"(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."
],
"topics": [
"complex-analysis",
"mathematics",
"number-theory",
"sciences"
],
"translations": [
{
"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": "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"
}
],
"wikipedia": [
"imaginary unit"
]
}
],
"word": "imaginary unit"
}
{
"etymology_text": "So named because it takes on the role of unit for the imaginary part of a complex number.",
"forms": [
{
"form": "imaginary units",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "imaginary unit (plural imaginary units)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with quotations",
"Japanese terms with redundant script codes",
"Korean terms with redundant script codes",
"en:Complex analysis",
"en:Number theory"
],
"examples": [
{
"ref": "2013, J. A. Sparenberg, Hydrodynamic Propulsion and Its Optimization, Springer, page 183",
"text": "In Section 4.3 we introduced the imaginary unit i with (i)²#x3D;-1, in the complex space domain. In section 4.4 we introduced the complex unit j with (j)²#x3D;-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.",
"type": "quotation"
},
{
"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."
},
{
"ref": "2021, Bruce Hunt, Locally Mixed Symmetric Spaces, Springer, page 123",
"text": "Consider now in addition to the given #x5C;H#x5C;subset#x5C;mathbb#x7B;O#x7D;, one of the totally imaginary units not contained in #x5C;H, and note that #x7B;SU#x7D;(2) acts transitively on the set of totally imaginary units of a quaternion algebra; as we are assuming #x5C;alpha#x5C;notin#x5C;H, we may in fact assume that #x5C;mathbb#x7B;O#x7D;#x3D;#x5C;H#x5C;oplus#x5C;H' with #x5C;alpha#x5C;in#x5C;H'.",
"type": "quotation"
}
],
"glosses": [
"An imaginary number (in the case of complex numbers, usually denoted i) that is defined as a solution to the equation x²=-1."
],
"links": [
[
"number theory",
"number theory"
],
[
"complex analysis",
"complex analysis"
],
[
"imaginary number",
"imaginary number"
],
[
"complex number",
"complex number"
],
[
"solution",
"solution"
],
[
"equation",
"equation"
]
],
"qualifier": "quaternion theory",
"raw_glosses": [
"(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."
],
"topics": [
"complex-analysis",
"mathematics",
"number-theory",
"sciences"
],
"wikipedia": [
"imaginary unit"
]
}
],
"translations": [
{
"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": "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"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-09 from the enwiktionary dump dated 2024-05-02 using wiktextract (4d5d0bb and edd475d). 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.
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