Find the absolute values of z if 2z-i +5 = 3z -3i +1

Given the complex
equation:

2z -i + 5 = 3z -3i
+1

We need to find the absolute value of
z.

First we need to rewrite z into the format of the
complex number z = a+bi

let us combine terms with z on the
left side.

==> 2z -3z = -3i +1 +i
-5

==> -z = -4 -2i

Now
we will multiply by -1

==> z = 4 +
2i

Now we will calculate the absolute
values.

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

               = sqrt( 4^2 +
2^2)

               = sqrt(16 + 4) = sqrt20 =
2sqrt5

==> l zl =
2sqrt5