# How do you find abs(-4 - sqrt2i)?

Jul 19, 2016

$\left\mid - 4 - \sqrt{2} i \right\mid = \textcolor{g r e e n}{3 \sqrt{2}}$

#### Explanation:

The absolute value of a complex number is the distance of the point represented by that number in the complex plane from the complex plain origin.

This distance can be calculated using the Pythagorean Theorem.

For the given complex number $- 4 - \sqrt{2} i$
this distance is
$\textcolor{w h i t e}{\text{XXX}} \sqrt{{\left(- 4\right)}^{2} + {\left(- \sqrt{2}\right)}^{2}} = \sqrt{16 + 2} = \sqrt{18} = 3 \sqrt{2}$