2002 AMC 12A Problem 24

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

\text{(A) }1001 \qquad \text{(B) }1002 \qquad \text{(C) }2001 \qquad \text{(D) }2002 \qquad \text{(E) }2004

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.