# How do you simplify abs(-12 + 22.5i)?

Jan 10, 2016

Please go through the steps given below.

#### Explanation:

If $z = a + i b$ is a complex number then $| z | = \sqrt{{a}^{2} + {b}^{2}}$

Our problem is $| - 12 + 22.5 i |$

The modulus is found by the rule mentioned above

$| - 12 + 22.5 i | = \sqrt{{\left(- 12\right)}^{2} + {\left(22.5\right)}^{2}}$

$| - 12 + 22.5 i | = \sqrt{144 + 506.25}$

$| - 12 + 22.5 i | = \sqrt{650.25}$

$| - 12 + 22.5 i | = 25.5$