1. Complex modules in mathematics. The value of the positive square root of the sum of squares of the real part and imaginary part of a complex number is called the module of a complex number.

2. In the fields of linear algebra, functional analysis and related mathematics, a module is a function in which all vectors in a vector space are given non-zero positive lengths or sizes.

The algorithms of these two modules are as follows:

1, let the complex number z=a+bi(a, b∈R).

Then the module of complex number z | z| = √ a 2+b 2.

Its geometric meaning is the distance from a point (a, b) on the complex plane to the origin. ?

2. The modular operator "%"is used to calculate the remainder of the division of two numbers.

A%b, where a and b are integers.

The calculation rule is that a is divided by b, and the remainder is the result of modulo.

For example: 100% 17?

100 = 17*5+ 15

So 100% 17 = 15.

Extended data:

| z 1 z2| = |z 1| |z2|

┃| z 1 |-| z2|┃≤| z 1+z2 |≤| z 1 |+| z2 |

| z1| z1-z2 | =| z1z2 || is the formula of the distance between two points on the complex plane, from which the equations of lines, circles, hyperbolas, ellipses and parabolas on the complex plane can be derived.

In abstract algebra, the concept of modules over rings is a generalization of the concept of vector space. Here, the scalar is no longer required to be located in a domain, but can be located in any ring.

Therefore, a module is an additive Abel group like a vector space; The product between ring elements and module elements is defined, which conforms to the law of association (when used with multiplication in rings) and distribution.

Modules are closely related to the representation theory of groups. They are also the central concepts of commutative algebra and homology algebra, and are widely used in algebraic geometry and algebraic topology.

A ring (r,+,+,...) includes an Abelian group (m,+) and an operator m? ×? r？ -& gt； ? m？ (called scalar multiplication or product of numbers, usually expressed as rx, r? ∈? R and x? ∈? M) Yes, all R, S? ∈? r，？ x，y？ ∈? m，x(rs) = (xr)s，x(r+s) =？ xr+xs，(x+y)r？ =? xr+yr，x 1？ =? Similarly, x can define the left R- module of a ring.