What is the absolute value of z if 3z -9i = 8i + z + 4.

3z = 9i = 8i + z + 4

We need
to determine the absolute value of.

First let us determine
z as a form of the complex number z = a + bi

First we will
combine like terms.

==> 3z - z = 8i - 9i +
4

==> 2z = 4 - i

Now we
will divide by 2.

==> z = (4-i)
/2

==> z = 2 - (1/2)
i

Now that we wrote z into the standard form, we will
calculate the absolute value.

We know
that:

l z l = sqrt( a^2 +
b^2).

==> l z l = sqrt( 2^2 +
(1/2)^2

              = sqrt( 4 +
1/4)

               = sqrt(17/4) = sqrt17 /
2

==> l z l = sqrt17 /
2

Then, the absolute value of
z is sqrt17 / 2