Absolute value |x| is the distance of a number from zero on the number line, always non-negative. |3| = 3, |−3| = 3, |0| = 0. In complex numbers, absolute value is the distance from the origin: |a+bi| = √(a²+b²).
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Pro Tip
To solve |f(x)| = k: split into f(x) = k and f(x) = −k. For |f(x)| < k: solve −k < f(x) < k. For |f(x)| > k: solve f(x) < −k or f(x) > k.
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Did You Know?
Absolute value is central to error analysis, machine learning loss functions (MAE — Mean Absolute Error), and the L1 norm. In optimization, the L1 norm creates "sparse" solutions — useful in data compression and feature selection.
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