Find the number of ordered pairs of real numbers $(a,b)$ such that $(a + bi)^{2002} = a - bi$.
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
Find the number of ordered pairs of real numbers $(a,b)$ such that $(a + bi)^{2002} = a - bi$.
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2004
Find the number of ordered pairs of real numbers $(a,b)$ such that $(a + bi)^{2002} = a - bi$.
train