Question

How do you simplify `abs(19i )`?

Answer 1

`|19i| = 19`

Explanation:

Given a complex number `x+iy` we have the complex modulus (the complex analog of an absolute value) defined to be
`|x+iy| = sqrt(x^2 + y^2)`

Thus

`|19i| = |0+19i| = sqrt(0^2 + 19^2) = 19`

Note that the complex modulus may also be viewed geometrically as the distance from a given point to the origin on the complex plane. Then, as `19i` lies on one of the axes, we can immediately tell that the modulus of `19i` will be the coefficient `19`.