de Moivre's formula

proper noun

A formula that connects trigonometry and complex numbers, stating that, for any complex number (and, in particular, for any real number) x and integer n, big ( cos (x)+i sin (x) big )ⁿ= cos (nx)+i sin (nx), where i is the imaginary unit.

Similar
de Moivre's identityde Moivre's theorem
Ask AI about this wordChatGPTClaudePerplexityGoogle AIGrok

Meanings

proper noun
  1. mathematicsA formula that connects trigonometry and complex numbers, stating that, for any complex number (and, in particular, for any real number) x and integer n, big ( cos (x)+i sin (x) big )ⁿ= cos (nx)+i sin (nx), where i is the imaginary unit.

    Synonyms: de Moivre's identity, de Moivre's theorem

Synonyms & antonyms

proper nounA formula that connects trigonometry and complex numbers, stating that, for any complex number (and, in particular, for any real number) x and integer n, big ( cos (x)+i sin (x) big )ⁿ= cos (nx)+i sin (nx), where i is the imaginary unit.

Similar
de Moivre's identityde Moivre's theorem
Also see
de moivre's identityde moivre's theorem

Origin

Named after Abraham de Moivre (1667–1754), French mathematician.

Full word history & related roots →
Cite this entry
APA

de Moivre's formula. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/de%20Moivre's%20formula

MLA

“de Moivre's formula.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/de%20Moivre's%20formula. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “de Moivre's formula,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/de%20Moivre's%20formula.

Source: de Moivre's formula on Wiktionary, CC BY-SA 4.0.