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

1 Answer
Dec 16, 2015

#|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#.