Determine the absolute value of complex number z if z-2z'=2-4i? z=x+i*y z'=x-i*y

First, we'll have to determine the complex number z and
then, we'll determine the absolute value, |z|.

z - 2z' = 2
- 4i

We'll substitute z and z' by their
expressions:

x + i*y - 2(x - i*y) = 2 -
4i

x + i*y - 2x + 2i*y = 2 -
4i

We'll combine the real parts and the imaginary
parts:

(x - 2x)+i*(y + 2y) = 2 - 4i (from
enunciation)

Comparing, we'll
get:

x - 2x=2

-x =
2

x = -2

y + 2y =
-4

3y = -4

y =
-4/3

The complex number is:
z=-2-4i/3

It's absolute
value is:

|z| = sqrt[Re(z)^2 +
Im(z)^2]

|z| = sqrt[(-2)^2 +
(-4/3)^2]

|z| = sqrt ((4 +
16)/9)

|z| = sqrt ((36+
16)/9)

|z| = sqrt
(52/9)

The absolute value of the complex
number is |z| = sqrt (52/9).