Primary
Imaginary Unit (i) ❍｜Definition｜1st｜20251119205401-00-⌔
Imaginary unit
The imaginary unit, usually denoted by i, is a mathematical constant that is a solution to the quadratic equation x = −1, which is not solved by any real number. Any real-number multiple of the imaginary unit is called an imaginary number.
By combining the real numbers with the imaginary unit using addition and multiplication, a new number system known as the complex numbers is formed; it consists of all numbers of the form a + bi with real numbers a and b.
There are two complex square roots of −1: the imaginary unit i and its additive inverse − i. More generally, every nonzero complex number has two distinct complex-valued square roots, which are additive inverses of each other, while zero has only zero as its (double) square root.
Historically, the imaginary unit was denoted by , though this is now rare. In contexts in which use of the letter i is ambiguous or problematic, the letter j is sometimes used instead. For example, in electrical engineering the imaginary unit is normally denoted by j instead of i, because i is commonly used to denote electric current.1
Printed 2026-06-28.
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Link to original Footnotes
Stubbings, George Wilfred (1945). Elementary vectors for electrical engineers. London: I. Pitman. p. 69. Boas, Mary L. (2006). Mathematical Methods in the Physical Sciences (3rd ed.). New York [u.a.]: Wiley. p. 49. ISBN 0-471-19826-9. ↩
Secondary
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