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Question:

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

n=20 and Re(z)=-10

n=20 and Re(z)=10

n=40 and Re(z)=10

n=40 and Re(z)=-10

Solution:

Correct option is C.
n=40 and Re(z)=-10
Put z = x + 10i
∴ \frac{2(x+10i)-n}{2(x+10i)+n} = (2i-1).
compare real and imaginary coefficients
x=-10, n=40.