# Magnitude

A magnitude is a measure of the size of a mathematical entity. For example, the magnitude of a complex number is the distance from the number (graphed on the complex plane) to the origin, a measure of the size of a complex number. The magnitude is generally a positive real number.

Formulaically, the magnitude of a real number $x$ is its absolute value $|x|$, sometimes written $\sqrt{x^2}$. The magnitude $|z|$ of a complex number $z$ equals $\sqrt{\mathrm {Re}(z)^2 + \mathrm{Im}(z)^2}$. Both types of magnitude are bound by a form of the Triangle Inequality which states that $|a| + |b| \geq |a + b|$.