# absolute value

## absolute value

*noun*

## Definition of *ABSOLUTE VALUE*

**:**Â a nonnegative number equal in numerical value to a given real number

**:**Â the positive square root of the sum of the squares of the real and imaginary parts of a complex number

## First Known Use of *ABSOLUTE VALUE*

## absolute value

*noun*

*(Concise Encyclopedia)*

Measure of the magnitude of a real number, complex number, or vector. Geometrically, the absolute value represents (absolute) displacement from the origin (or zero) and is therefore always nonnegative. If a real number *a* is positive or zero, its absolute value is itself; if *a* is negative, its absolute value is *a*. A complex number *z* is typically represented by an ordered pair (*a*, *b*) in the complex plane. Thus, the absolute value (or modulus) of *z* is defined as the real number , which corresponds to *z*’s distance from the origin of the complex plane. Vectors, like arrows, have both magnitude and direction, and their algebraic representation follows from placing their “tail” at the origin of a multidimensional space and extracting the corresponding coordinates, or components, of their “point.” The absolute value (magnitude) of a vector is then given by the square root of the sum of the squares of its components. For example, a three-dimensional vector *v*, given by (*a*, *b*, *c*), has absolute value . Absolute value is symbolized by vertical bars, as in

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