# How do you find abs( 8i )?

Jun 22, 2016

$| 8 i | = 8$

#### Explanation:

The modulus of a complex number $a + b i$, denoted $| a + b i |$, represents that number's distance from the origin on the complex plane, and is given by

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

Then, for our given number, we have

$| 8 i | = | 0 + 8 i | = \sqrt{{0}^{2} + {8}^{2}} = \sqrt{64} = 8$

Note that this is as intuition tells us, as $8 i$ is $8$ units from the origin along the imaginary axis on the complex plane.