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title
| title |
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| Absolute Value |
Absolute Value
Absolute value is the non-negative value of a number, whether that number is positive or negative. You can think of a number's absolute value as its distance from zero. It can be also be considered as magnitude without direction. It can be defined as,
The absolute value of a quantity x is denoted by |x| (the quantity is enclosed between two vertical bars). 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.
For complex numbers, this is also referred to as the modulus.
Pythagorean Theorem: If z=a+bi, where a=Re{z} and b=Im{z}, then |z|=sqrt(a^2+b^2)
Examples
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Simplify |-5|
|-5| = 5
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Simplify |0(5)|
|0(5)| = |0| = 0
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Simplify -|-1|
-|-1| = -(1) = -1
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Simplify |-5(-3) + 1|
|-5(-3) + 1| = |15 + 1| = |16| = 16
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Simplify |8|
|8| = 8
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Simplify |(-5)^3|
|(-5)^3| = |-125| = 125
- Simplify -|(4)^2| -|16| = -16