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Absolute value

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The absolute value of a real number is defined as:

[math]\displaystyle{ |x| = x }[/math] when [math]\displaystyle{ x\geq 0 }[/math]

[math]\displaystyle{ |x| = -x }[/math] when [math]\displaystyle{ x\lt 0 }[/math]

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

[math]\displaystyle{ |z| = \sqrt{x^2+y^2} }[/math]

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.

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