# How do you find abs( -3 i )?

Oct 27, 2016

$\left\mid - 3 i \right\mid = 3$

#### Explanation:

The absolute value of a number is its distance from the origin,
So if we take our complex number with cartesian coordinates,

$\left(0 , - 3\right)$ or $0 - 3 i$

to work out its distance we use Pythagoras's theorem.

${c}^{2} = {a}^{2} + {b}^{2}$

with c=abs(("a , b)")

so to find out c,

$c = \sqrt{{a}^{2} + {b}^{2}}$

$c = \sqrt{{\left(0\right)}^{2} + {\left(- 3\right)}^{2}}$

$c = \sqrt{9}$

$c = 3$

$\left\mid - 3 i \right\mid = 3$