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(2z - n)/(2z + n) = 2i - 1 with Im(z) = 10: find n and Re(z)

The same question, asked 2 times: 14 May 2024 S2, 25 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    14 May 2024 S2

    108
    Let z∈Cz \in \mathbb{C} with Im(z)=10\text{Im}(z) = 10 and it satisfies 2z−n2z+n=2i−1\frac{2z-n}{2z+n} = 2i-1 for some natural number n, then

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  2. Question 2

    25 Apr 2025 S1

    129
    Let z be the complex number with Im(z)=10Im(z) = 10 and satisfying 2z−n2z+n=2i−1\frac{2z-n}{2z+n}= 2i- 1, where i=−1i=\sqrt{- 1}, for some natural number ' nn ' then

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