# How do you find abs(-2 + 4i )?

Mar 31, 2016

$| - 2 + 4 i | = 2 \sqrt{5}$

#### Explanation:

The modulus of a complex number $a + b i$ is defined as

$| a + b i | = \sqrt{{a}^{2} + {b}^{2}}$

(Note that this is the distance from the origin to the point $\left(a , b\right)$ on the complex plane)

In this case, that gives us

$| - 2 + 4 i | = \sqrt{{\left(- 2\right)}^{2} + {4}^{2}}$

$= \sqrt{4 + 16}$

$= \sqrt{20}$

$= 2 \sqrt{5}$