# How do you find the absolute value of -8i?

Jan 31, 2017

$8$

#### Explanation:

Given a complex number like $z = x + i y$ then $\left\mid z \right\mid$ is defined as

abs z = sqrt(z cdot \bar z where $\overline{z} = x - i y$ is the $z$ conjugate.

Then $\left\mid z \right\mid = \sqrt{{x}^{2} + {y}^{2}}$. In our case

$\left\mid - i 8 \right\mid = \sqrt{\left(- i 8\right) \left(i 8\right)}$ = 8

$\left\mid z \right\mid \ge 0$ by definition.