**r**= x**i**+y**j**+z**k**,

It should be noted that the modulus of a vector is a scalar.

**Modulus** is also a synonym for:

- the absolute value of a complex number, defined to be the distance between the origin and the complex number, thought of as a point in the plane.
- the absolute value of a real number
- the number by which two numbers are said to be congruent in modular arithmetic. A related, incorrect use of 'modulus' is for the remainder after integer division (see below).

In computer programming, the **modulus** operator gives the remainder of integer division, ie modular arithmetic. Mathematicians tend to call this **modulo**, for example:

- 13 = 3 modulo 10
- 13 = 3 mod 10

C programmers will write:

- 13 % 10 = 3.