Imaginary unit

The imaginary unit, usually denoted by i, is a mathematical constant that is a solution to the quadratic equation x2 = −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 ⁠ − 1 {\displaystyle {\sqrt {-1}}} ⁠, 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.