# How do you find abs(4 + 5i)?

Apr 9, 2016

$| 4 + 5 i | = \sqrt{41}$

#### Explanation:

Given a complex number $a + b i$, we define the modulus of the number, denoted $| a + b i |$ as

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

In this case, that gives us

$| 4 + 5 i | = \sqrt{{4}^{2} + {5}^{2}} = \sqrt{41}$