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

We have the given equation z = 2z' - 3 +
5i

Let z = a + ib

z = 2z' - 3
+ 5i

=> a + ib = 2a - 2b*i - 3 +
5i

=> a + ib = 2a - 3 - 2b*i +
5i

equate the real and complex
coefficients

=> a = 2a - 3 and b = 5 -
2b

=> a = 3 and 3b =
5

z = 3 + (5/3)i

The absolute
value is sqrt (3^2 + (5/3)^2)

=> sqrt (9 +
25/9)

=> sqrt (
106/9)

=> (sqrt
106)/3

The absolute value of z is (sqrt
106)/3