Phrase guide

imaginary number

noun · 3 senses · updated from the 2026-07-25 local source snapshot

Definitions and examples are grouped by meaning. Pronunciation, history, word forms, translations, descendants, synonyms, antonyms, derived terms, and related words appear whenever the source provides them.

Sound

Pronunciation

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1

noun

Meaning 1

A number of the form bi, where b is any real number and i denotes the imaginary unit.

Definition source: English Wiktionary via Wiktextract

Usage: strict-sense

Topics: complex-analysis, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

2

noun

Meaning 2

A number of the form a + bi, where a and b are real numbers and b is nonzero.

Definition source: English Wiktionary via Wiktextract

Usage: broadly

Topics: complex-analysis, mathematics, sciences

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: none provided

Antonyms: none provided

3

noun

Meaning 3

(mathematics) a number of the form a+bi where a and b are real numbers and i is the square root of -1

Definition source: Princeton WordNet 3.0

No example sentence was provided for this meaning.

Meaning relationships

Synonyms: complex number, complex quantity, imaginary

Antonyms: none provided

Broader terms: number

Narrower terms: complex conjugate, real number, real, pure imaginary number

History

Etymology

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.

Across languages

Translations

51 source translations are retained for this English entry.

  • Armenian: կեղծ թիվ (keġc tʻiv) — number of the form bi
  • Bengali: অবাস্তব সংখ্যা (obastob śoṅkha) — number of the form bi
  • Bulgarian: имагине́рно число́ (imaginérno čisló) — number of the form bi
  • Catalan: nombre imaginari — number of the form bi
  • Chinese Cantonese: 虛數 /虚数 (heoi1 sou3) — number of the form bi
  • Chinese Mandarin: 虛數 /虚数 (xūshù) — number of the form bi
  • Chinese Mandarin: 純虛數 /纯虚数 (chúnxūshù) — number of the form bi
  • Czech: imaginární číslo — number of the form bi
  • Danish: imaginært tal — number of the form bi
  • Dutch: imaginair getal — number of the form bi
  • Esperanto: imaginara nombro — number of the form bi
  • Finnish: imaginaariluku — number of the form bi
  • Finnish: imaginääriluku — number of the form bi
  • French: nombre imaginaire pur — number of the form bi
  • Georgian: წარმოსახვითი რიცხვი (c̣armosaxviti ricxvi) — number of the form bi
  • German: rein imaginäre Zahl — number of the form bi
  • German: imaginäre Zahl — number of the form bi
  • Greek: φανταστικός αριθμός (fantastikós arithmós) — number of the form bi
  • Hebrew: מספר מרוכב — number of the form bi
  • Hungarian: képzetes szám — number of the form bi
  • Hungarian: imaginárius szám — number of the form bi
  • Icelandic: þvertala — number of the form bi
  • Japanese: 虚数 (kyosū) — number of the form bi
  • Kazakh: жорамал сан (joramal san) — number of the form bi
  • Khmer: ចំនួននិម្មិត (cɑmnuənnimmɨt) — number of the form bi
  • Korean: 허수 (heosu) — number of the form bi
  • Latin: quantitas imaginaria — number of the form bi
  • Latin: numerus imaginarius — number of the form bi
  • Latvian: imaginārs skaitlis — number of the form bi
  • Malayalam: അവാസ്തവികസംഖ്യ (avāstavikasaṅkhya) — number of the form bi
  • Māori: tau pohewa — number of the form bi
  • Persian: عدد موهومی — number of the form bi
  • Polish: liczba urojona — number of the form bi
  • Portuguese: número imaginário — number of the form bi
  • Portuguese: número puramente imaginário — number of the form bi
  • Russian: мни́мое число́ (mnímoje čisló) — number of the form bi
  • Serbo-Croatian: imaginarni broj — number of the form bi
  • Spanish: número imaginario — number of the form bi
  • Swedish: imaginärt tal — number of the form bi
  • Tagalog: gunimbilang — number of the form bi
  • Thai: จํานวนจินตภาพ (jam-nuuan-jin-dtà-pâap) — number of the form bi
  • Turkish: sanal sayı — number of the form bi
  • Ukrainian: уя́вне число́ (ujávne čysló) — number of the form bi
  • Vietnamese: số ảo — number of the form bi
  • Vietnamese: số thuần ảo — number of the form bi
  • Bulgarian: компле́ксно число́ (kompléksno čisló) — number of the form a + bi, with b ≠ 0
  • Chinese Mandarin: 虛數 /虚数 (xūshù) — number of the form a + bi, with b ≠ 0
  • Finnish: imaginaariluku — number of the form a + bi, with b ≠ 0
  • Finnish: imaginääriluku — number of the form a + bi, with b ≠ 0
  • French: nombre imaginaire — number of the form a + bi, with b ≠ 0
  • Polish: liczba zespolona — number of the form a + bi, with b ≠ 0