If the module is presented in the form of a continuous function, then the value of its argument can be both positive and negative: |x| = x, x ≥ 0; |x| = - x, x < 0. Consequently, the number in brackets, accepts any character.
Module zero is zero, and the module is any positive number – to him. If the argument is negative, then after opening the brackets, its sign changes from minus to plus. Based on this, the conclusion follows that the modules of opposite integers is equal to: |x| = |x| = x.
The module of a complex number is given by: |a| = √b 2 + c 2, and |a + b| ≤ |a| + |b|. If the argument is present in multiples of a positive integer, it can be taken out of the sign brackets, for example: |4*b| = 4*|b|.
The negative module can not be, therefore, any negative number is converted to positive: |x| = x, |-2| = 2, |-1/7| = 1/7, |-2,5| = 2,5.
If the argument is in the form of complex numbers, for computational convenience it is allowed to change the order of the member expressions, enclosed in square brackets: |2-3| = |3-2| = 3-2 = 1, since (2-3) is less than zero.
Raised to the power of argument at the same time is under the root sign are of the same order – it is solved by using module: √a2 = |a| = ±a.
If you face the problem, which does not indicate a condition of disclosure of the brackets module, to get rid of them is not necessary – this will be the end result. But if you want to reveal them, it is necessary to indicate sign ±. For example, you need to find the value of √(2 * (4-b)) 2. His decision as follows: √(2 * (4-b)) 2 = |2 * (4-b)| = 2 * |4-b|. Since the expression of 4-b is unknown, it should be left in brackets. If you add an additional condition, for example, |4-b| > 0, then the end result 2 * |4-b| = 2 *(4 - b). As the unknown element can also be set to a specific number, which should be taken into consideration because it will affect the sign of the expression.