# How do you find the distance on a complex plane from 5-12i to the origin?

$\left\mid z \right\mid = \sqrt{{x}^{2} + {y}^{2}}$ with $x = R e \left(z\right)$ and $y = I m \left(z\right)$ is the distance of $z$ to the origin (think of $\left\mid z \right\mid$ as $\left\mid z - 0 \right\mid$).
So the distance from $5 - 12 i$ to the origin is $\left\mid 5 - 12 i \right\mid = \sqrt{{5}^{2} + {\left(- 12\right)}^{2}} = \sqrt{25 + 144} = \sqrt{169}$