# Absolute value

### From Conservapedia

The **absolute value** of a number is a measure of the size of that number. The absolute value of *x* is written | *x* | .

- If
*x*is a positive number, then |*x*| =*x*.

- If
*x*is a negative number, then |*x*| = −*x*.

- If
*x*= 0 then |*x*| = 0.

Absolute value has several useful properties. One is the *multiplicative* property. If *x* and *y* are two numbers, then . Another is the *triangle inequality*, which is the fact that . For example, if *x* = 3 and *y* = − 5, then | *x* + *y* | = | 3 + ( − 5) | = | 3 − 5 | = | − 2 | = 2, while | *x* | + | *y* | = | − 5 | + | 3 | = 5 + 3 = 8. In this case, the triangle inequality is the fact that 2 is not more than 8.

Complex numbers also have an absolute value (sometimes called the modulus). If *z* = *x* + *i**y* is a complex number with real part *x* and imaginary part *y*, then . If we represent *z* as a point in the complex plane with coordinates (*x*,*y*), then | *z* | is the distance from this point to the origin. The absolute value of complex numbers also has the multiplicative property and satisfies the triangle inequality.