Question

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

• A. n = 20 and $\text{Re}(z) = -10$
• B. n = 40 and $\text{Re}(z) = -10$
• C. n = 40 and $\text{Re}(z) = 10$
• D. n = 20 and $\text{Re}(z) = 10$

Hint:

When solving equations involving complex numbers, always express the complex number in the form $x+iy$ and then equate the real and imaginary parts on both sides of the equation. Remember that $i^2 = -1$.

Answer 1

The Correct Option is B