54 lines
1.6 KiB
Markdown
54 lines
1.6 KiB
Markdown
---
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title: Absolute Value
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---
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## Absolute Value
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Absolute value is the non-negative value of a number, whether that number is positive or negative.
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You can think of a number's absolute value as its distance from zero.
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It can be defined as,
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<img src="https://upload.wikimedia.org/wikipedia/commons/thumb/6/6b/Absolute_value.svg/2000px-Absolute_value.svg.png" width="300">
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The absolute value of a quantity x is denoted by |x| (the quantity is enclosed between two vertical bars).
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Here you can see that in the graph of y = |x|, if -2 is input in to the function, 2 is the result. This is because -2 has a distance of 2 from zero. The absolute value of a number can never be negative.
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For complex numbers, this is also referred to as the *modulus*.
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```
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Pythagorean Theorem: If z=a+bi, where a=Re{z} and b=Im{z}, then |z|=sqrt(a^2+b^2)
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```
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### Examples
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* **Simplify |-5|**
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|-5| = 5
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* **Simplify |0(5)|**
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|0(5)| = |0| = 0
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* **Simplify -|-1|**
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-|-1| = -(1) = -1
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* **Simplify |-5(-3) + 1|**
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|-5(-3) + 1| = |15 + 1| = |16| = 16
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* **Simplify |8|**
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|8| = 8
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* **Simplify |(-5)^3|**
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|-125| = 125
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#### More Information:
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[Purplemath](https://www.purplemath.com/modules/absolute.htm)
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