# How do you find abs(1 + 3i)?

Apr 14, 2016

$| 1 + 3 i | = \sqrt{10}$

#### Explanation:

We define the modulus of a complex number $a + b i , a , b \in \mathbb{R}$, denoted $| a + b i |$, as

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

In this case, we have

$| 1 + 3 i | = \sqrt{{1}^{2} + {3}^{2}} = \sqrt{10}$