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 $\lfloor 100n \rfloor$ ?