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Line 1: − The '''modulus''' function provides the remainder of division. For example, in 5 / 3 the remainder is 2.+ − + + + + + + + + + + + + + + +
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::''For the term relating to complex numbers, see [[Complex number]].''
[[category:operators]]
Aside from its unrelated use in complex numbers, the term '''modulus''' refers to the [[remainder]], that is, the remainder of integer [[division]]. For example, in 11 / 3 the remainder is 2. This could be stated as <math>mod(11, 3) = 2\,</math>, though mathematicians much more commonly express it as "11 is congruent to 2 modulo 3" and write it symbolically as "<math>11 \equiv 2\mod 3</math>".
The notion of congruence is actually more general than the remainder function. We could also say "2 is congruent to 11 modulo 3", or "<math>2 \equiv 11\mod 3</math>".
"<math>x \equiv y\mod k</math>" means that <math>x - y\,</math> is an integer multiple of <math>k\,</math>.
The remainder operation is also important in computer programming, and the term "modulus" is used to refer to this operation. In [[C programming language|C]]-like languages it is denoted with a percent sign:
::::x = 11 % 3; // x is now 2
In [[complex number]]s, the modulus is the analogue of the absolute value, given by <math>|a+bi| = \sqrt{a^2 + b^2}</math>.
[[Category:Mathematics]]
[[Category:Programming Languages]]