{"status": "success", "data": {"description_md": "The complex numbers $z$ and $w$ satisfy the system\n$z+\\frac{20i}{w}=5+i$\n$w+\\frac{12i}{z}=-4+10i.$\\\nFind the smallest possible value of $|zw|^2$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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>The complex numbers <span class=\"katex--inline\">z</span> and <span class=\"katex--inline\">w</span> satisfy the system<br/>&#10;<span class=\"katex--inline\">z+\\frac{20i}{w}=5+i</span><br/>&#10;<span class=\"katex--inline\">w+\\frac{12i}{z}=-4+10i.</span><br/>&#10;Find the smallest possible value of <span class=\"katex--inline\">|zw|^2</span>.</p>&#10;<hr/>&#10;<p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2012 AIME II Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/12_aime_II_p09", "prev": "/problem/12_aime_II_p07"}}