imaginary number


Definition of imaginary number

: a complex number (such as 2 + 3i) in which the coefficient of the imaginary unit is not zero

called also imaginary

— compare pure imaginary

Examples of imaginary number in a Sentence

Recent Examples on the Web Because no real number x satisfies the equation x2+ 1 = 0, mathematicians built a new number system—now known as the complex numbers—by adding an imaginary number i and imposing the stipulation that i2 + 1= 0. Emily Riehl, Scientific American, 17 Sep. 2021 Math has many important constants that give the discipline structure, like pi and i, the imaginary number equal to the square root of -1. Avery Thompson, Popular Mechanics, 2 Mar. 2021 That’s an appropriate label, because an imaginary number consists of the square root of a negative number, which by definition does not exist. John Horgan, Scientific American, 7 Jan. 2021 The wave function has embedded within it an imaginary number. John Horgan, Scientific American, 7 Jan. 2021 Each of these energy levels, En, corresponds to a zero of the form Zn = ½ + iEn, which has a real part equal to ½ and an imaginary part formed by multiplying En by the imaginary number i. Quanta Magazine, 4 Apr. 2017 The symmetries of these matrices usually guarantee that imaginary numbers cancel out and the eigenvalues are real, so that these matrices make sense as descriptions of physical systems. Quanta Magazine, 4 Apr. 2017 If imaginary numbers have always seemed strange to you, prepare for a change in perspective. Quanta Magazine, 14 Feb. 2019 For example, the solutions to x5 = 1 are five points on a circle when plotted onto a graph comprised of real numbers along one axis and imaginary numbers on the other. Davide Castelvecchi, Scientific American, 20 Mar. 2018

These example sentences are selected automatically from various online news sources to reflect current usage of the word 'imaginary number.' Views expressed in the examples do not represent the opinion of Merriam-Webster or its editors. Send us feedback.

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First Known Use of imaginary number

1798, in the meaning defined above

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Time Traveler for imaginary number

Time Traveler

The first known use of imaginary number was in 1798

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Dictionary Entries Near imaginary number


imaginary number

imaginary part

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Statistics for imaginary number

Last Updated

28 Oct 2021

Cite this Entry

“Imaginary number.” Dictionary, Merriam-Webster, Accessed 5 Dec. 2021.

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