# How do you find abs(5-2i)?

Jul 17, 2016

$| 5 - 2 i | = \sqrt{29}$

#### Explanation:

The modulus of a complex number $a + b i$, denoted as $| a + b i |$, is given by

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

and represents the distance of that number from the origin on the complex plane.

For our given number, then, we have

$| 5 - 2 i | = \sqrt{{5}^{2} + {\left(- 2\right)}^{2}}$

$= \sqrt{25 + 4}$

$= \sqrt{29}$