Complex Number Equal Imaginary Parts

1675AdeptComplex NumbersAlgebra

AIME I · 2007 · Problem 3

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?

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Complex Number Equal Imaginary Parts

1675AdeptComplex NumbersAlgebra

AIME I · 2007 · Problem 3

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?

0 students attempted0% solvedRating 1675