imaginary number

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imaginary number

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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.

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 ${\displaystyle a=0}$, then ${\displaystyle x=ib}$ 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.

• 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.

• (sensu stricto): purely imaginary number

• (both senses): complex number

• (sensu lato): purely imaginary number

• complex number
• real number

• Imaginary number on Encyclopedia of Mathematics
• Imaginary Number on Wolfram MathWorld