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AoPS Wiki:Problem of the Day/September 11, 2011

Find the number of ordered pairs of real numbers $(a,b)$ such that $(a + bi)^{2002} = a - bi$.

$\textbf{(A)}$ 1001 $\textbf{(B)}$ 1002 $\textbf{(C)}$ 2001 $\textbf{(D)}$ 2002 $\textbf{(E)}$ 2004

Source: AMC 12

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