Quadratic or something else

Algebra Level 3

\[iz^{2}=1+\frac{2}{z}+\frac{3}{z^{2}}+\frac{4}{z^{3}}+\frac{5}{z^{4}} + \ldots \]

If \(z = n \pm \sqrt{-i} \) satisfy the series above. Find the value of \(n\).

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