imaginary number

noun

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

called also imaginary

compare pure imaginary

Example Sentences

Recent Examples on the Web

Complex numbers have two parts, one real and one imaginary, the latter of which relates to the imaginary number i, defined as the square root of −1. —Kevin Hartnett, Quanta Magazine, 13 Jan. 2022

Physicist Richard Feynman once predicted that number 137 defines the table’s outer limit; adding any more protons would produce an energy that could be quantified only by an imaginary number, rendering element 138 and higher impossible. —Rebecca Coffey, Discover Magazine, 29 Nov. 2011

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

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Word History

First Known Use

1798, in the meaning defined above