What is the absolute values of z is 3z-1 = z -i + 5

Q: What is the absolute value of z is 3z-1 = z -i +
5.

Solution:

If z = x+iy, then
the absolute value of z = |z| = (x^2+y^2)^(1/2), where x and y are
real.

We first solve for z from the given equation 3z-1 =
z-i+5.

Subtract z-1:

3z-z =
-i+5 +1

 2z = 6-i which is x+iy
form

So absilote  z = |z| = {6^+
(-1)^2}^(1/2)

|z| = (36+1}^(1/2) =
37^(1/2).

Therefore absolute value of z =
37^(1/2).