A Disguise of Something Else

Algebra Level 3

iz2=1+2z+3z2+4z3+5z4+ iz^2=1+\dfrac 2z + \dfrac{3}{z^2}+\dfrac{4}{z ^3}+\dfrac{5}{z^4}+\cdots

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

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