# absolute value

Absolute value is the value of a number without regard to
its sign. The absolute value, or **modulus**, of a real
number, *r*, is just the distance of the number from zero measured
along the real number line, and is denoted
|*r* | (read "mod *r* "). Being a distance, it can't be
negative; so, for example, |3| = |-3| = 3.

The same idea applies to the absolute value of a complex
number *a* + *ib*, except that, in this case, the complex
number is represented by a point on an Argand
diagram. The absolute value, |*a* + *ib*|, is the length of
the line from the origin to the given point, and is equal to √(*a*^{2} + *b*^{2}).