Question

How do you find `abs(-5i)`?

Answer 1

Apply the definition `|a+bi| = sqrt(a^2+b^2)` to find that

`|-5i| = 5`

Explanation:

The modulus of a complex number `a+bi`, denoted `|a+bi|`, is given by

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

and is an extension of the absolute value function, which applies to reals. The latter represents the distance from the real number to `0` on the number line, and the former represents the distance of the complex number to the origin on the complex plane.

Applying this definition to our given complex number, we have:

`|-5i| = |0+(-5)i|`

`=sqrt(0^2+(-5)^2)`

`=sqrt(0+25)`

`=sqrt(25)`

`=5`