{"status": "success", "data": {"description_md": "The complex numbers $z$ and $w$ satisfy the system<br>\\begin{align*}z+\\frac{20i}{w}&=5+i,\\\\w+\\frac{12i}{z}&=-4+10i.\\end{align*}Find 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/>\\begin{align*}z+\\frac{20i}{w}&amp;=5+i,\\w+\\frac{12i}{z}&amp;=-4+10i.\\end{align*}Find the smallest possible value of <span class=\"katex--inline\">|zw|^2</span>.</p>&#10;<hr><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>", "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"}}