Question

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

Answer 1

Calculate its module.

Explanation:

`absz = sqrt(x^2 + y^2)` with `x = Re(z)` and `y = Im(z)` is the distance of `z` to the origin (think of `absz` as `abs(z - 0)`).

So the distance from `5-12i` to the origin is `abs(5-12i) = sqrt(5^2 + (-12)^2) = sqrt(25 + 144) = sqrt(169)`