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

Given the expression:

2z ; z'
= 3+ 2i

We need to find the absolute value of
z.

First we will need to rewrite z using the form z =a+
bi

Then z' = a- bi.

Let us
substitute.

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

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

==> a + 3bi = 3+
2i

==> a = 3

==>
b= 2/3

==> z = 3 + 2/3
*i

Now we will calculate the absolute
value.

We know that:

l zl =
sqrt(a^2 + b^2)

==> l z l = sqrt(3^2 + (2/3)^2 =
sqrt( 9 + 4/9) = sqrt(85/9)

==> Then
the absolute value for z is l z l = sqrt(85/9) = sqrt(85) /
3