# How do you find abs( 4+7i )?

Oct 18, 2016

The absolute value of $4 + 7 i$ is $\sqrt{65}$.

#### Explanation:

The absolute value of a complex number in the form $a + b i$ is found using this process: $\sqrt{{a}^{2} + {b}^{2}}$.

So, given $z = | 4 + 7 i |$,

$| z | = \sqrt{{4}^{2} + {7}^{2}}$
$| z | = \sqrt{16 + 49}$
$| z | = \sqrt{65}$