Imaginary unit (nonfiction)

i in the complex or cartesian plane. Real numbers lie on the horizontal axis, and imaginary numbers lie on the vertical axis.

The imaginary unit or unit imaginary number (i) is a solution to the quadratic equation x2 + 1 = 0. There is no real number with this property, hence the term imaginary.

i can be used to extend the real numbers to what are called complex numbers, using addition and multiplication. A simple example of the use of i in a complex number is 2 + 3i.

Imaginary numbers are an important mathematical concept, which extend the real number system ℝ to the complex number system ℂ, which in turn provides at least one root for every nonconstant polynomial P(x).

There are two complex square roots of −1, namely i and −i, just as there are two complex square roots of every real number other than zero, which has one double square root.

In contexts where i is ambiguous or problematic, j or the Greek ι is sometimes used. In the disciplines of electrical engineering and control systems engineering, the imaginary unit is normally denoted by j instead of i, because i is commonly used to denote electric current.

Fiction cross-reference

• Crimes against mathematical constants
• Gnomon algorithm
• Gnomon Chronicles
• Mathematician
• Mathematics

Nonfiction cross-reference

• Mathematics (nonfiction)

External links:

• Imaginary unit @ Wikipedia