How to Calculate Absolute Value

What is Absolute Value?

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).

Step-by-Step Guide

1. 1|x| = x if x ≥ 0; |x| = −x if x < 0
2. 2|x − y| = distance between x and y on the number line
3. 3Triangle inequality: |a + b| ≤ |a| + |b|
4. 4Properties: |ab| = |a||b|, |a/b| = |a|/|b|, |a|² = a²

Worked Examples