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# Absolute Value

## What is the Absolute Value?

The absolute value of a number refers to its distance from zero on the number line. Whether the number is positive or negative. It is represented by vertical bars or pipes enclosing the number, such as |b|, and is defined as follows:

• If b is a positive number, then |b| = b.
• If b is a negative number, then |b| = -b (the opposite of b).
• If b is zero, then |b| = 0.

The absolute value of an integer b is indicated as |b| and is given by ## Absolute Value Symbol

the absolute value symbol is represented by vertical bars or pipes enclosing the number or equation. The symbol is denoted as ||b|| or |b| and is read as “the absolute value of b”. The vertical bars indicate that the value inside the bars is to be taken as a positive value, regardless of its sign.

For example, |6| = 6, |-4| = 4, and |0| = 0.

For instance, |b – 3| means “the absolute value of the difference between b and 3”.

If b – 3 is positive, then |b – 3| = b – 3. If b – 3 is negative, then |b – 3| = -(b – 3) = 3 – b.

### The absolute value of a Number Examples

Here are some examples of finding the absolute value of a number:

• |-7| = 7: The absolute value of -7 is 7.
• |4| = 4: The absolute value of 4 is 4.
• |-2.5| = 2.5: The absolute value of -2.5 is 2.5.
• |0| = 0: The absolute value of 0 is 0.
• |2 – 8| = |-6| = 6: The absolute value of the difference between 2 and 8 is 6 because.
• |-3 + 5i| = √((-3)2 + 52) = √(9 + 25) = √34.

### Absolute Value Function

The absolute value function is a mathematical function that maps each real number to its non-negative value. It is represented by |b| and defined as:

• | b | = b, if b ≥ 0
• | b | = -b, if b < 0

#### Frequently Asked Questions on Absolute Values

Q: What is the absolute value of a negative number?
A: The absolute value of a negative number is the opposite of that number. For example, the absolute value of -7 is |-7| = 7.

Q: What is the absolute value of zero?
A: The absolute value of zero is zero.

Q: What is the absolute value of a fraction?
A: The absolute value of a fraction is the absolute value of its numerator divided by the absolute value of its denominator.
For example, the absolute value of -3/4 is |-3|/|4| = 3/4.

Q: What is the absolute value of a complex number?
A: The absolute value of a complex number a + bi is the distance from the origin to the point (a, b) in the complex plane. It is calculated as |a + bi| = sqrt(x2 + b^2).

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