Mock AIME 2 2006-2007 Problems/Problem 5

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Given that $\displaystyle  iz^2=1+\frac 2z + \frac{3}{z^2}+\frac{4}{z ^3}+\frac{5}{z^4}+\cdots$ and $\displaystyle z=a\pm \sqrt{b+i},$ find $\displaystyle  \lfloor 100ab \rfloor.$

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