# How do you find abs( sqrt11 + i sqrt(5))?

May 30, 2016

Use the definition of a modulus $| a + b i | = \sqrt{{a}^{2} + {b}^{2}}$ to find that

$| \sqrt{11} + \sqrt{5} i | = 4$

#### Explanation:

Given a complex number $a + b i$, the modulus of that number, denoted $| a + b i |$, is given by

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

This is analogous to the absolute value of a real number, giving the distance of the complex number from the origin on the complex plane, rather than the distance from $0$ on the number line.

For our given value, then, we have

$| \sqrt{11} + \sqrt{5} i | = \sqrt{{\left(\sqrt{11}\right)}^{2} + {\left(\sqrt{5}\right)}^{2}}$

$= \sqrt{11 + 5}$

$= \sqrt{16}$

$= 4$