How to calculate the number module

The module of number is an absolute value which registers with use of vertical brackets: |kh |. Visually it can be presented as the piece postponed in any direction from zero.

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If the module is presented in the form of continuous function, value of her argument can be both positive, and negative: |kh | = x, x? 0; |kh | = - x, x 2

The module of zero is equal to zero, and the module of any positive number – to him. If the argument negative, after removal of brackets its sign changes from minus on plus. On the basis of it the conclusion follows that modules of opposite numbers are equal: | - x | = |kh | = x. 3

The module of complex number is on a formula: |a | = vb? + c?, and |a + b |? |a | + |b |. If in argument there is at a type of a multiplier the whole positive number, it can be taken out for a bracket sign, for example: |4*b | = 4 * | b |. 4

Negative the module cannot be therefore any negative number will be transformed to the 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, for convenience of calculations 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: va? = |a | = ±a. 7

If before you a task in which the condition of removal of brackets of the module is not specified, it is not necessary to get rid of them is and there will be an end result. And if it is required to open them, it is necessary to specify a sign ±. For example, it is necessary to find value of expression of v (2 * (4-b))?. Its decision looks as follows: v (2 * (4-b))? = |2 * (4-b) | = 2 * |4-b |. As the expression sign 4-b is unknown, it is necessary to leave it in brackets. If to add an additional condition, for example, |4-b |> 0, 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 an expression sign can be also set.