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

Given the complex number 3z+i = 2z -i +
5.

We need to find the absolute values for
z.

First, we need to rewrite z as a complex number into the
form z= a+ bi.

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

We will combine like
terms.

==> 3z - 2z + i + i - 5 =
0

==> z +2i - 5 = 0

Now
we will isolate z on the left side.

==> z = 5 -
2i

Then , a= 5  and b =
-2

Then the absolute value for z is given
by:

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

==> l z l = sqrt( 5^2 +
-2^2)

            = sqrt( 25+ 4) =
sqrt29.

Then, the absolute value for z is l z
l = sqrt29.