What is the absolute value of z if 2z- z' = 3+4i?

To determine the absolute value of z, we'll have to determine
first, the real part and the imaginary part of z.

z = a +
bi

Re(z) = a and Im(z) = b

z' is the
conjugate of z, therefore z = a+ bi and z' = a - bi

2(a+bi) - a + bi
= 3 + 4i

2a + 2bi - a + bi= 3 + 4i

a +
3bi = 3 + 4i

Comparing both sides, we'll get: a = 3 and 3b = 4
=> b = 4/3

The absolute value of
z:

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

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

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

The absolute value is: |z| =
(sqrt97)/3