# How to open the module?

The module of a number in another way is still called absolutethe value of this number. In the event that there is a real number under the sign of the module, then before revealing the module, it is necessary to find out whether it is negative or positive.

- If our number is positive, then it does not change when the module is expanded, if the number is negative, then it is multiplied by -1:

| x | = x, (if x is greater than or equal to zero);

| x | = -x (if x is less than zero).

- Accordingly, after the module is expanded, we always get a number that is greater than zero.
- If the vector a = (xa, ya) was placed under the module symbol, then the length of the given vector will be the module in this case. And it is defined as follows:

| a | = 2xa2 + ya2.

- If the component is greater than two, then all of them are placed under the sign of the radical and are squared.
- The complex number z = x + iy has a module that is found, like in a two-dimensional vector:

| z | = 2x2 + y2.

As you can see, no matter how manyis an expression that stands under the sign of the module (real, complex or vector), the module will always have a real value equal to the "length" of the number if it is "drawn" in the coordinate system. Well, we coped with the solution of the problem of how to open a number module.