See imaginary unit on Wiktionary
{
"etymology_text": "So named because it takes on the role of unit for the imaginary part of a complex number.",
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{
"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": "quote"
},
{
"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": "quote"
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"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": [
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"number theory",
"number theory"
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"complex analysis",
"complex analysis"
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[
"imaginary number",
"imaginary number"
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"complex number",
"complex number"
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"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",
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"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"
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],
"word": "imaginary unit"
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{
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"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": "quote"
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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."
},
{
"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'.",
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"glosses": [
"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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"(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": [
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"mathematics",
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"wikipedia": [
"imaginary unit"
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"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"
}
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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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