The module of number is an absolute value which registers with use of vertical brackets: |x|. Visually it can be presented as the piece postponed in any direction from zero.
Instruction
1. If the module is presented in the form of continuous function, then the value of her argument can be both positive, and negative: |x| = x, x ≥ 0; |x| = - x, x
The module of zero is equal to zero, and the module of any positive number – to him. If the argument negative, then after removal of brackets its sign changes from minus on plus. On the basis of it a conclusion follows that modules of opposite numbers are equal: | - x | = |x| = x.
The module of complex number is on a formula: |a| = √b² + with², and | a + b | ≤ |a| + |b|. If in an argument is present at a type of a multiplier the whole positive number, then it can be taken out for the sign of a bracket, for example: |4*b| = 4 * |b|.
Negative the module cannot be therefore any negative number will be transformed to positive: | - x | = x, |-2| = 2, |-1/7| = 1/7, |-2.5| = 2.5.
If the argument is presented in the form of difficult number, then for convenience of calculations the change of an order of members of the expression concluded in rectangular brackets is allowed: |2-3| = |3-2| = 3-2 = 1, as (2-3) less than zero.
The argument built in degree at the same time is under the sign of a root of the same order – it is solved by means of the module: √a² = |a| = ±a.
If before you a task in which the condition of removal of brackets of the module is not specified then it is not necessary to get rid of them - it is and there will be an end result. And if it is required to reveal them, then it is necessary to specify the sign ±. For example, it is necessary to find value of expression √ (2 * (4-b))². Its decision looks as follows: √ (2 * (4-b))² = | 2 * (4-b) | = 2 * |4-b|. As the sign of expression 4-b is unknown, it is necessary to leave it in brackets. If to add an additional condition, for example, |4-b|> 0, then as a result it will turn out 2 * |4-b| = 2 * (4 - b). As an unknown element the concrete number which should be taken into account since it will influence the sign of expression can be also set.
2. The module of zero is equal to zero, and the module of any positive number – to him. If the argument negative, then after removal of brackets its sign changes from minus on plus. On the basis of it a conclusion follows that modules of opposite numbers are equal: | - x | = |x| = x.
3. The module of complex number is on a formula: |a| = √b² + with², and | a + b | ≤ |a| + |b|. If in an argument is present at a type of a multiplier the whole positive number, then it can be taken out for the sign of a bracket, for example: |4*b| = 4 * |b|.
4. Negative the module cannot be therefore any negative number will be transformed to positive: | - x | = x, |-2| = 2, |-1/7| = 1/7, |-2.5| = 2.5.
5. If the argument is presented in the form of difficult number, then for convenience of calculations the change of an order of members of the expression concluded in rectangular brackets is allowed: |2-3| = |3-2| = 3-2 = 1, as (2-3) less than zero.
6. The argument built in degree at the same time is under the sign of a root of the same order – it is solved by means of the module: √a² = |a| = ±a.
7. If before you a task in which the condition of removal of brackets of the module is not specified then it is not necessary to get rid of them - it is and there will be an end result. And if it is required to reveal them, then it is necessary to specify the sign ±. For example, it is necessary to find value of expression √ (2 * (4-b))². Its decision looks as follows: √ (2 * (4-b))² = | 2 * (4-b) | = 2 * |4-b|. As the sign of expression 4-b is unknown, it is necessary to leave it in brackets. If to add an additional condition, for example, |4-b|> 0, then as a result it will turn out 2 * |4-b| = 2 * (4 - b). As an unknown element the concrete number which should be taken into account since it will influence the sign of expression can be also set.