{"status": "success", "data": {"description_md": "Suppose that $x$, $y$, and $z$ are complex numbers such that $xy = -80-320i$, $yz = 60$, and $zx = -96+24i$, where $i = \\sqrt{-1}$. Then there are real numbers $a$ and $b$ such that $x+y+z = a+bi$. Find $a^2 + b^2$.\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>Suppose that <span class=\"katex--inline\">x</span>, <span class=\"katex--inline\">y</span>, and <span class=\"katex--inline\">z</span> are complex numbers such that <span class=\"katex--inline\">xy = -80-320i</span>, <span class=\"katex--inline\">yz = 60</span>, and <span class=\"katex--inline\">zx = -96+24i</span>, where <span class=\"katex--inline\">i = \\sqrt{-1}</span>. Then there are real numbers <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> such that <span class=\"katex--inline\">x+y+z = a+bi</span>. Find <span class=\"katex--inline\">a^2 + b^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": 3, "problem_name": "2018 AIME II Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/18_aime_II_p06", "prev": "/problem/18_aime_II_p04"}}