Question

How do you find `abs( 6-3i )`?

Answer 1

`3sqrt5`

Explanation:

`"given a complex number "z=x+yi" then"`

`•color(white)(x)|z|=|x+yi|=sqrt(x^2+y^2)`

`"here "x=6" and "y=-3`

`rArr|6-3i|=sqrt(36+9)=sqrt45=3sqrt5`

Answer 2

`3sqrt 5`

Explanation:

Any complex no. of the form `z = x+iy` has `|z| =sqrt( x^2 + y^2)`
So, here x = 6, y = -3.
So we get:
`|z| = sqrt(6^2 + (-3)^2) = sqrt(36 + 9) = sqrt(45) = 3sqrt5`