Solve the following systems of equations:

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Question:

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

  1. $\mathrm{n}=20$ and $\operatorname{Re}(\mathrm{z})=-10$

  2. $\mathrm{n}=20$ and $\operatorname{Re}(\mathrm{z})=10$

  3. $\mathrm{n}=40$ and $\operatorname{Re}(\mathrm{z})=-10$

  4. $\mathrm{n}=40$ and $\operatorname{Re}(\mathrm{z})=10$

Correct Option: , 3

Solution:

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