MathDB

Complex Number Problem

Source: AIME I 2007 #3

March 15, 2007

AMC

Problem Statement

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 equal, find

b

.

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