{"status": "success", "data": {"description_md": "Find the number of ordered pairs of real numbers $(a,b)$ such that $(a+bi)^{2002} = a-bi$.\n\n$\\text{(A) }1001<br>\\qquad<br>\\text{(B) }1002<br>\\qquad<br>\\text{(C) }2001<br>\\qquad<br>\\text{(D) }2002<br>\\qquad<br>\\text{(E) }2004$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Find the number of ordered pairs of real numbers  <span class=\"katex--inline\">(a,b)</span>  such that  <span class=\"katex--inline\">(a+bi)^{2002} = a-bi</span> .</p>&#10;<p> <span class=\"katex--inline\">\\text{(A) }1001\\qquad\\text{(B) }1002\\qquad\\text{(C) }2001\\qquad\\text{(D) }2002\\qquad\\text{(E) }2004</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2002 AMC 12A Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/02_amc12A_p25", "prev": "/problem/02_amc12A_p23"}}