# imaginary number

noun

## 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 Math has many important constants that give the discipline structure, like pi and i, the imaginary number equal to the square root of -1. That’s an appropriate label, because an imaginary number consists of the square root of a negative number, which by definition does not exist. The wave function has embedded within it an imaginary number. 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. 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. If imaginary numbers have always seemed strange to you, prepare for a change in perspective. 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.

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.

## First Known Use of imaginary number

1798, in the meaning defined above

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## The first known use of imaginary number was in 1798

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## Statistics for imaginary number

Last Updated

14 Mar 2021

Cite this Entry

“Imaginary number.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/imaginary%20number. Accessed 14 Apr. 2021.

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