# Absolute Value Function

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An Absolute Value Function of any real number is always its positive value

$|x| =\left\{\begin{array}{ll}x \quad\textrm{for} \quad x \geq 0\\-x \quad\textrm{for}\quad x \lt 0\end{array}\right.$
• Example(s):
• |-3|=3
• $|(3,0,4)|=\sqrt{3^2+0^2+4^2}=5$
• $|3+i4|=\sqrt{3^2+4^2}=5$
• Counter-Example(s):

## References

### 2016

$|x|=xsgn(x)$
where sgn(x) is the sign function. The absolute value is therefore always greater than or equal to 0. (...) The absolute value of a complex number $z=x+iy$, also called the complex modulus,