# 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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