Find the absolute value of z is z= (2i-1)/(3+4i).

Given the complex number z =
(2i-1)/(3+4i)

We need to find the absolute values of z = l
z l.

First we need to simplify z and rewrite into the
standard form z= a+ bi.

First we will multiply both
numerator and denominator by (3-4i).

==> z =
(-1+2i)(3-4i)/(3+4i)(3-4i)

         = (-3 +4i +6i -8i^2)/(9
-16i^2)

But we know that i^2 =
-1

==> z = ( -3+10i
+8)/(9+16)

          = ( 5+10i) /
25

==> z = (1/5) +
(2/5)i

Now we will calculate the absolute
values.

We know that l zl =
sqrt(a^2+b^2)

==> l z l = sqrt(1/5)^2 +
(2/5)^2

                = sqrt(1+4)/25 = sqrt5 /
5

==> l z l = sqrt5 / 5 =
1/sqrt5