Question

How do you find `abs( 8i )`?

Answer 1

`|8i| = 8`

Explanation:

The modulus of a complex number `a+bi`, denoted `|a+bi|`, represents that number's distance from the origin on the complex plane, and is given by

`|a+bi| = sqrt(a^2+b^2)`

Then, for our given number, we have

`|8i| = |0+8i| = sqrt(0^2+8^2) = sqrt(64) = 8`

Note that this is as intuition tells us, as `8i` is `8` units from the origin along the imaginary axis on the complex plane.