A Disguise of Something Else

Algebra Level 3

\[ iz^2=1+\dfrac 2z + \dfrac{3}{z^2}+\dfrac{4}{z ^3}+\dfrac{5}{z^4}+\cdots\]

For \(i = \sqrt{-1}\), a complex number, \(z=n\pm \sqrt{-i}\) satisfy the equation above. What is the value of \(\lfloor 100n \rfloor\)?

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