The absolute value of a real number is its distance from 0 on the number line. A complex number's absolute value is also a measure of its distance from zero. However, instead of measuring this distance on the number line, a complex number's absolute value is measured from zero on the complex number plane.

In general

### Illustrated **Example**

To find the absolute value of the complex number, 3 + 4*i*, we find the distance from zero to that number on the plane.

**Practice** Problems

$$ |3 + 2i| = \sqrt{3^2 + (2)^2} \\ = \sqrt{9 + 4} \\ = \sqrt{13} $$

$$ |3 - 2i| = \sqrt{3^2 + (\red{-}2)^2} \\ = \sqrt{9 + \red{4}} \\ = \sqrt{13} $$

$$ |-5 -3i| = \sqrt{(-3)^2 + (-5)^2} \\ = \sqrt{9 + 25} \\ = \sqrt{34} $$

$$ | -x - ci| = \sqrt{(-x)^2 + (-c)^2} \\ = \sqrt{x^2 + c^2} $$