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# Absolute value

The absolute value of a real number is defined as:

$\displaystyle{ |x| = x }$ when $\displaystyle{ x\geq 0 }$

$\displaystyle{ |x| = -x }$ when $\displaystyle{ x\lt 0 }$

The absolute value of a complex number z = x + iy is defined as:

$\displaystyle{ |z| = \sqrt{x^2+y^2} }$

where we take the positive value of the square root. Note that when y = 0, both definitions are equivalent.

Geometrically, the absolute value of a number represents its distance from the origin.