AIME 2007a Problem 3

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Answer

The complex number $z$ is equal to $9+bi$ , where $b$ is a positive real number and $i^{2}=-1$ . Given that the imaginary parts of $z^{2}$ and $z^{3}$ are the same, what is $b$ equal to?

Dataset text AIME 1983 to 2026. Quoted with source.

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