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 into 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.

In the News

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  A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. "Re" is the real axis, "Im" is the imaginary axis, and i satisfies i2 = −1.

Fiction cross-reference

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

Nonfiction cross-reference

• Complex number (nonfiction)
• Imaginary number (nonfiction) - a complex number that can be written as a real number multiplied by the imaginary unit i,[note 1] which is defined by its property i2 = −1.
• Mathematics (nonfiction)
• Real number (nonfiction)

External links:

• Imaginary unit @ Wikipedia