How do you find abs( -3 i )|3i|?

1 Answer
Oct 27, 2016

abs(-3i) =3|3i|=3

Explanation:

The absolute value of a number is its distance from the origin,
So if we take our complex number with cartesian coordinates,

(0,-3)(0,3) or 0-3i03i

to work out its distance we use Pythagoras's theorem.

c^2=a^2+b^2c2=a2+b2

with c=abs(("a , b)")c=|(a , b))|

so to find out c,

c=sqrt(a^2+b^2)c=a2+b2

c=sqrt((0)^2+(-3)^2)c=(0)2+(3)2

c=sqrt(9)c=9

c=3c=3

abs(-3i) =3|3i|=3