See imaginary number on Wiktionary
{
"etymology_text": "The adjective imaginary in this context was first used (as French imaginaire) by René Descartes in 1673, La Geometrie, referring to imaginary numbers in the broad sense, as non-real roots of polynomials. Descartes' usage was derogatory, but the concept later gained acceptance through the work of Leonhard Euler and Carl Friedrich Gauss in the 18th century.",
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"_dis1": "54 46",
"sense": "purely imaginary number",
"word": "sensu lato"
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"ref": "2008, Donald A. McQuarrie, Mathematics for Physical Chemistry: Opening Doors, University Science Books, page 54:",
"text": "If a#x3D;0, then x#x3D;ib is called an imaginary number. The message here is that we must introduce imaginary numbers in order to be able to solve quadratic equations in general.",
"type": "quote"
}
],
"glosses": [
"A number of the form bi, where b is any real number and i denotes the imaginary unit."
],
"id": "en-imaginary_number-en-noun-O5DNOYMo",
"links": [
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"complex analysis"
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"real number"
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[
"imaginary unit",
"imaginary unit"
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"(complex analysis, strict sense) A number of the form bi, where b is any real number and i denotes the imaginary unit."
],
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{
"_dis1": "69 31",
"word": "complex number"
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{
"_dis1": "69 31",
"word": "real number"
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"tags": [
"strict-sense"
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"mathematics",
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"translations": [
{
"_dis1": "60 40",
"code": "hy",
"lang": "Armenian",
"roman": "keġc tʻiv",
"sense": "number of the form bi",
"word": "կեղծ թիվ"
},
{
"_dis1": "60 40",
"code": "bn",
"lang": "Bengali",
"roman": "obastob śoṅkha",
"sense": "number of the form bi",
"word": "অবাস্তব সংখ্যা"
},
{
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"code": "ca",
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"word": "nombre imaginari"
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"code": "yue",
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"sense": "number of the form bi",
"word": "虛數"
},
{
"_dis1": "60 40",
"code": "yue",
"lang": "Chinese Cantonese",
"roman": "heoi¹ sou³",
"sense": "number of the form bi",
"word": "虚数"
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"_dis1": "60 40",
"code": "cmn",
"lang": "Chinese Mandarin",
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"word": "虛數"
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{
"_dis1": "60 40",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "xūshù",
"sense": "number of the form bi",
"word": "虚数"
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"_dis1": "60 40",
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "number of the form bi",
"word": "純虛數"
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{
"_dis1": "60 40",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "chúnxūshù",
"sense": "number of the form bi",
"word": "纯虚数"
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{
"_dis1": "60 40",
"code": "cs",
"lang": "Czech",
"sense": "number of the form bi",
"tags": [
"neuter"
],
"word": "imaginární číslo"
},
{
"_dis1": "60 40",
"code": "da",
"lang": "Danish",
"sense": "number of the form bi",
"tags": [
"neuter"
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"word": "imaginært tal"
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{
"_dis1": "60 40",
"code": "nl",
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"sense": "number of the form bi",
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"neuter"
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"word": "imaginair getal"
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{
"_dis1": "60 40",
"code": "eo",
"lang": "Esperanto",
"sense": "number of the form bi",
"word": "imaginara nombro"
},
{
"_dis1": "60 40",
"code": "fi",
"lang": "Finnish",
"sense": "number of the form bi",
"word": "imaginaariluku"
},
{
"_dis1": "60 40",
"code": "fi",
"lang": "Finnish",
"sense": "number of the form bi",
"word": "imaginääriluku"
},
{
"_dis1": "60 40",
"code": "fr",
"lang": "French",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "nombre imaginaire pur"
},
{
"_dis1": "60 40",
"code": "ka",
"lang": "Georgian",
"roman": "c̣armosaxviti ricxvi",
"sense": "number of the form bi",
"word": "წარმოსახვითი რიცხვი"
},
{
"_dis1": "60 40",
"code": "de",
"lang": "German",
"sense": "number of the form bi",
"tags": [
"feminine"
],
"word": "rein imaginäre Zahl"
},
{
"_dis1": "60 40",
"code": "de",
"english": "sensu stricto",
"lang": "German",
"sense": "number of the form bi",
"tags": [
"feminine"
],
"word": "imaginäre Zahl"
},
{
"_dis1": "60 40",
"code": "el",
"lang": "Greek",
"roman": "fantastikós arithmós",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "φανταστικός αριθμός"
},
{
"_dis1": "60 40",
"code": "he",
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"sense": "number of the form bi",
"word": "מספר מרוכב"
},
{
"_dis1": "60 40",
"code": "hu",
"lang": "Hungarian",
"sense": "number of the form bi",
"word": "képzetes szám"
},
{
"_dis1": "60 40",
"code": "hu",
"lang": "Hungarian",
"sense": "number of the form bi",
"word": "imaginárius szám"
},
{
"_dis1": "60 40",
"code": "is",
"lang": "Icelandic",
"sense": "number of the form bi",
"word": "þvertala"
},
{
"_dis1": "60 40",
"alt": "きょすう",
"code": "ja",
"lang": "Japanese",
"roman": "kyosū",
"sense": "number of the form bi",
"word": "虚数"
},
{
"_dis1": "60 40",
"code": "kk",
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"roman": "joramal san",
"sense": "number of the form bi",
"word": "жорамал сан"
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{
"_dis1": "60 40",
"code": "km",
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"roman": "cɑmnuənnimmɨt",
"sense": "number of the form bi",
"word": "ចំនួននិម្មិត"
},
{
"_dis1": "60 40",
"alt": "虛數",
"code": "ko",
"lang": "Korean",
"roman": "heosu",
"sense": "number of the form bi",
"word": "허수"
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{
"_dis1": "60 40",
"code": "la",
"lang": "Latin",
"sense": "number of the form bi",
"tags": [
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],
"word": "quantitas imaginaria"
},
{
"_dis1": "60 40",
"code": "la",
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"sense": "number of the form bi",
"tags": [
"masculine"
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"word": "numerus imaginarius"
},
{
"_dis1": "60 40",
"code": "lv",
"lang": "Latvian",
"sense": "number of the form bi",
"word": "imaginārs skaitlis"
},
{
"_dis1": "60 40",
"code": "ml",
"lang": "Malayalam",
"roman": "avāstavikasaṅkhya",
"sense": "number of the form bi",
"word": "അവാസ്തവികസംഖ്യ"
},
{
"_dis1": "60 40",
"code": "mi",
"lang": "Maori",
"sense": "number of the form bi",
"word": "tau pohewa"
},
{
"_dis1": "60 40",
"code": "fa",
"lang": "Persian",
"sense": "number of the form bi",
"word": "عدد موهومی"
},
{
"_dis1": "60 40",
"code": "pl",
"lang": "Polish",
"sense": "number of the form bi",
"word": "liczba urojona"
},
{
"_dis1": "60 40",
"code": "pt",
"lang": "Portuguese",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "número imaginário"
},
{
"_dis1": "60 40",
"code": "pt",
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"sense": "number of the form bi",
"tags": [
"masculine"
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"word": "número puramente imaginário"
},
{
"_dis1": "60 40",
"code": "ru",
"lang": "Russian",
"roman": "mnímoje čisló",
"sense": "number of the form bi",
"tags": [
"neuter"
],
"word": "мни́мое число́"
},
{
"_dis1": "60 40",
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "imaginarni broj"
},
{
"_dis1": "60 40",
"code": "es",
"lang": "Spanish",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "número imaginario"
},
{
"_dis1": "60 40",
"code": "sv",
"lang": "Swedish",
"sense": "number of the form bi",
"word": "imaginärt tal"
},
{
"_dis1": "60 40",
"code": "tl",
"lang": "Tagalog",
"sense": "number of the form bi",
"word": "gunimbilang"
},
{
"_dis1": "60 40",
"code": "th",
"lang": "Thai",
"roman": "jam-nuuan-jin-dtà-pâap",
"sense": "number of the form bi",
"word": "จำนวนจินตภาพ"
},
{
"_dis1": "60 40",
"code": "tr",
"lang": "Turkish",
"sense": "number of the form bi",
"word": "sanal sayı"
},
{
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"code": "uk",
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"roman": "ujávne čysló",
"sense": "number of the form bi",
"tags": [
"neuter"
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},
{
"_dis1": "60 40",
"code": "vi",
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"sense": "number of the form bi",
"word": "số ảo"
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"_dis1": "60 40",
"code": "vi",
"lang": "Vietnamese",
"sense": "number of the form bi",
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"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "number of the form a + bi, with b ≠ 0",
"word": "虛數"
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{
"_dis1": "45 55",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "xūshù",
"sense": "number of the form a + bi, with b ≠ 0",
"word": "虚数"
},
{
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"code": "fi",
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"sense": "number of the form a + bi, with b ≠ 0",
"word": "imaginaariluku"
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"code": "fi",
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"sense": "number of the form a + bi, with b ≠ 0",
"word": "imaginääriluku"
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"code": "fr",
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"sense": "number of the form a + bi, with b ≠ 0",
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"René Descartes",
"imaginary number"
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"en:Numbers"
],
"etymology_text": "The adjective imaginary in this context was first used (as French imaginaire) by René Descartes in 1673, La Geometrie, referring to imaginary numbers in the broad sense, as non-real roots of polynomials. Descartes' usage was derogatory, but the concept later gained acceptance through the work of Leonhard Euler and Carl Friedrich Gauss in the 18th century.",
"forms": [
{
"form": "imaginary numbers",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "imaginary number (plural imaginary numbers)",
"name": "en-noun"
}
],
"hypernyms": [
{
"sense": "both senses",
"word": "complex number"
}
],
"hyponyms": [
{
"sense": "purely imaginary number",
"word": "sensu lato"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "complex number"
},
{
"word": "real number"
}
],
"senses": [
{
"categories": [
"English terms with quotations",
"en:Complex analysis"
],
"examples": [
{
"ref": "2008, Donald A. McQuarrie, Mathematics for Physical Chemistry: Opening Doors, University Science Books, page 54:",
"text": "If a#x3D;0, then x#x3D;ib is called an imaginary number. The message here is that we must introduce imaginary numbers in order to be able to solve quadratic equations in general.",
"type": "quote"
}
],
"glosses": [
"A number of the form bi, where b is any real number and i denotes the imaginary unit."
],
"links": [
[
"complex analysis",
"complex analysis"
],
[
"real number",
"real number"
],
[
"imaginary unit",
"imaginary unit"
]
],
"raw_glosses": [
"(complex analysis, strict sense) A number of the form bi, where b is any real number and i denotes the imaginary unit."
],
"tags": [
"strict-sense"
],
"topics": [
"complex-analysis",
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Complex analysis"
],
"glosses": [
"A number of the form a + bi, where a and b are real numbers and b is nonzero."
],
"links": [
[
"complex analysis",
"complex analysis"
],
[
"real number",
"real number"
]
],
"raw_glosses": [
"(complex analysis, broad sense) A number of the form a + bi, where a and b are real numbers and b is nonzero."
],
"tags": [
"broadly"
],
"topics": [
"complex-analysis",
"mathematics",
"sciences"
]
}
],
"sounds": [
{
"audio": "LL-Q1860 (eng)-Flame, not lame-imaginary number.wav",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/f/f1/LL-Q1860_%28eng%29-Flame%2C_not_lame-imaginary_number.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-imaginary_number.wav.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/f/f1/LL-Q1860_%28eng%29-Flame%2C_not_lame-imaginary_number.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-imaginary_number.wav.ogg"
}
],
"synonyms": [
{
"sense": "sensu stricto",
"word": "purely imaginary number"
}
],
"translations": [
{
"code": "hy",
"lang": "Armenian",
"roman": "keġc tʻiv",
"sense": "number of the form bi",
"word": "կեղծ թիվ"
},
{
"code": "bn",
"lang": "Bengali",
"roman": "obastob śoṅkha",
"sense": "number of the form bi",
"word": "অবাস্তব সংখ্যা"
},
{
"code": "ca",
"lang": "Catalan",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "nombre imaginari"
},
{
"code": "yue",
"lang": "Chinese Cantonese",
"sense": "number of the form bi",
"word": "虛數"
},
{
"code": "yue",
"lang": "Chinese Cantonese",
"roman": "heoi¹ sou³",
"sense": "number of the form bi",
"word": "虚数"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "number of the form bi",
"word": "虛數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "xūshù",
"sense": "number of the form bi",
"word": "虚数"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "number of the form bi",
"word": "純虛數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "chúnxūshù",
"sense": "number of the form bi",
"word": "纯虚数"
},
{
"code": "cs",
"lang": "Czech",
"sense": "number of the form bi",
"tags": [
"neuter"
],
"word": "imaginární číslo"
},
{
"code": "da",
"lang": "Danish",
"sense": "number of the form bi",
"tags": [
"neuter"
],
"word": "imaginært tal"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "number of the form bi",
"tags": [
"neuter"
],
"word": "imaginair getal"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "number of the form bi",
"word": "imaginara nombro"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "number of the form bi",
"word": "imaginaariluku"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "number of the form bi",
"word": "imaginääriluku"
},
{
"code": "fr",
"lang": "French",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "nombre imaginaire pur"
},
{
"code": "ka",
"lang": "Georgian",
"roman": "c̣armosaxviti ricxvi",
"sense": "number of the form bi",
"word": "წარმოსახვითი რიცხვი"
},
{
"code": "de",
"lang": "German",
"sense": "number of the form bi",
"tags": [
"feminine"
],
"word": "rein imaginäre Zahl"
},
{
"code": "de",
"english": "sensu stricto",
"lang": "German",
"sense": "number of the form bi",
"tags": [
"feminine"
],
"word": "imaginäre Zahl"
},
{
"code": "el",
"lang": "Greek",
"roman": "fantastikós arithmós",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "φανταστικός αριθμός"
},
{
"code": "he",
"lang": "Hebrew",
"sense": "number of the form bi",
"word": "מספר מרוכב"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "number of the form bi",
"word": "képzetes szám"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "number of the form bi",
"word": "imaginárius szám"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "number of the form bi",
"word": "þvertala"
},
{
"alt": "きょすう",
"code": "ja",
"lang": "Japanese",
"roman": "kyosū",
"sense": "number of the form bi",
"word": "虚数"
},
{
"code": "kk",
"lang": "Kazakh",
"roman": "joramal san",
"sense": "number of the form bi",
"word": "жорамал сан"
},
{
"code": "km",
"lang": "Khmer",
"roman": "cɑmnuənnimmɨt",
"sense": "number of the form bi",
"word": "ចំនួននិម្មិត"
},
{
"alt": "虛數",
"code": "ko",
"lang": "Korean",
"roman": "heosu",
"sense": "number of the form bi",
"word": "허수"
},
{
"code": "la",
"lang": "Latin",
"sense": "number of the form bi",
"tags": [
"feminine"
],
"word": "quantitas imaginaria"
},
{
"code": "la",
"lang": "Latin",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "numerus imaginarius"
},
{
"code": "lv",
"lang": "Latvian",
"sense": "number of the form bi",
"word": "imaginārs skaitlis"
},
{
"code": "ml",
"lang": "Malayalam",
"roman": "avāstavikasaṅkhya",
"sense": "number of the form bi",
"word": "അവാസ്തവികസംഖ്യ"
},
{
"code": "mi",
"lang": "Maori",
"sense": "number of the form bi",
"word": "tau pohewa"
},
{
"code": "fa",
"lang": "Persian",
"sense": "number of the form bi",
"word": "عدد موهومی"
},
{
"code": "pl",
"lang": "Polish",
"sense": "number of the form bi",
"word": "liczba urojona"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "número imaginário"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "número puramente imaginário"
},
{
"code": "ru",
"lang": "Russian",
"roman": "mnímoje čisló",
"sense": "number of the form bi",
"tags": [
"neuter"
],
"word": "мни́мое число́"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "imaginarni broj"
},
{
"code": "es",
"lang": "Spanish",
"sense": "number of the form bi",
"tags": [
"masculine"
],
"word": "número imaginario"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "number of the form bi",
"word": "imaginärt tal"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "number of the form bi",
"word": "gunimbilang"
},
{
"code": "th",
"lang": "Thai",
"roman": "jam-nuuan-jin-dtà-pâap",
"sense": "number of the form bi",
"word": "จำนวนจินตภาพ"
},
{
"code": "tr",
"lang": "Turkish",
"sense": "number of the form bi",
"word": "sanal sayı"
},
{
"code": "uk",
"lang": "Ukrainian",
"roman": "ujávne čysló",
"sense": "number of the form bi",
"tags": [
"neuter"
],
"word": "уя́вне число́"
},
{
"code": "vi",
"lang": "Vietnamese",
"sense": "number of the form bi",
"word": "số ảo"
},
{
"code": "vi",
"lang": "Vietnamese",
"sense": "number of the form bi",
"word": "số thuần ảo"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "number of the form a + bi, with b ≠ 0",
"word": "虛數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "xūshù",
"sense": "number of the form a + bi, with b ≠ 0",
"word": "虚数"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "number of the form a + bi, with b ≠ 0",
"word": "imaginaariluku"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "number of the form a + bi, with b ≠ 0",
"word": "imaginääriluku"
},
{
"code": "fr",
"lang": "French",
"sense": "number of the form a + bi, with b ≠ 0",
"word": "nombre imaginaire"
}
],
"wikipedia": [
"Carl Friedrich Gauss",
"Leonhard Euler",
"René Descartes",
"imaginary number"
],
"word": "imaginary number"
}
Download raw JSONL data for imaginary number meaning in All languages combined (10.3kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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.