# imaginary number

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### 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.

### Noun

imaginary number (plural imaginary numbers)

1. (complex analysis, strict sense) A number of the form bi, where b is any real number and i denotes the imaginary unit.
• 2008, Donald A. McQuarrie, Mathematics for Physical Chemistry: Opening Doors, University Science Books, page 54,
If $a=0$ , then $x=ib$ is called an imaginary number. The message here is that we must introduce imaginary numbers in order to be able to solve quadratic equations in general.
2. (complex analysis, broad sense) A number of the form a + bi, where a and b are real numbers and b is nonzero.

#### Usage notes

• The term is often used without rigorous definition, and at times inconsistently.
• Zero is considered both a real number and an imaginary number.
• When the broad sense is used, the term purely imaginary number (or pure imaginary number) may be used for an imaginary number in the strict sense.