How do you simplify abs(19i )?

Dec 16, 2015

$| 19 i | = 19$

Explanation:

Given a complex number $x + i y$ we have the complex modulus (the complex analog of an absolute value) defined to be
$| x + i y | = \sqrt{{x}^{2} + {y}^{2}}$

Thus

$| 19 i | = | 0 + 19 i | = \sqrt{{0}^{2} + {19}^{2}} = 19$

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 $19 i$ lies on one of the axes, we can immediately tell that the modulus of $19 i$ will be the coefficient $19$.