# How to open a module?

Galina Uneasy
April 4, 2013

The modulus of a number is also called the absolute value of this number. If there is a real number under the sign of the module, then before opening the module, you need 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 opening the module, we always get a number that is greater than zero.
• If the vector a = (xa, ya) stood under the module sign, then the module in this case will be the length of this vector. And it is defined as:

| a | = 2xa2 + ya2.

• If the component is more than two, then they all fit under the sign of the radical and are squared.
• The complex number z = x + iy has a module, which is found, as in the two-dimensional vector:

| z | = 2x2 + y2.

As you can see, no matter what number is an expression standing under the module sign (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 the module numbers.