Question

Let $z \in C$ with Im(z) = 10 and it satisfies $\frac{2z-n}{2z+n} = 2i -1$ for some natural number $n$.Then :

• A. n = 20 and Re(z) = - 10
• B. n = 20 and Re(z) = 10
• C. n = 40 and Re(z) = - 10
• D. n = 40 and Re(z) = 10

Answer 1

Answer: (C)

n = 40 and Re(z) = - 10

Answer 2

Put $z = x + 10i$
$\therefore 2(x + 10i) - n = (2i - 1) . [2(x+10i) + n]$
compare real and imaginary coefficients
$x = - 10, n = 40$