Concepts
i (The Imaginary Unit)
the letter I, said as its own name
Also Known As j (Engineering Notation)
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Defined as a square root of negative one, a number no real number can be, since the square of any real number is never negative. Italian mathematician Rafael Bombelli worked with such quantities as a formal bookkeeping device as early as 1572, and Rene Descartes coined the very term imaginary in 1637, using it dismissively, to describe a quantity he regarded as fictitious and only useful for calculation. Leonhard Euler introduced the letter i for the quantity in 1777, and Carl Friedrich Gauss's later work helped establish the complex numbers, ordinary pairs of a real part and an i-multiplied part, as a fully legitimate and geometrically meaningful number system rather than a mere calculating fiction.
Facts
Origin YearDates Euler's introduction of the letter i as notation; Bombelli had already worked formally with such quantities as early as 1572, and Descartes coined the term imaginary in 1637, both well before Euler's notation. Cross-Tradition Connections
Associated With
Introduced the letter i as the standard notation, 1777.
Coined the term imaginary in 1637, dismissively, regarding such quantities as fictitious.
In Branch
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Frequently Asked Questions
If i is not a real number, is it just made up?
No more than any other number; it is a consistent, useful extension of the number system, not a trick.
Every number in mathematics is a human invention in the same sense i is, including the real numbers and even zero; the question that matters is whether a number system is consistent and useful, not whether it can be counted on physical fingers. Italian mathematician Rafael Bombelli worked with quantities like i as a formal bookkeeping device as early as 1572, and the imaginary unit has since become indispensable in electrical engineering, quantum mechanics and signal processing, well beyond a bookkeeping trick.
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