{"status": "success", "data": {"description_md": "Let $P$ be the product of the roots of $z^6+z^4+z^3+z^2+1=0$ that have positive imaginary part, and suppose that $P=r(\\cos \\theta^\\circ+i\\sin \\theta^\\circ),$ where $0<r$ and $0\\le \\theta <360.$ Find $\\theta.$\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>Let <span class=\"katex--inline\">P</span> be the product of the roots of <span class=\"katex--inline\">z^6+z^4+z^3+z^2+1=0</span> that have positive imaginary part, and suppose that <span class=\"katex--inline\">P=r(\\cos \\theta^\\circ+i\\sin \\theta^\\circ),</span> where <span class=\"katex--inline\">0&lt;r</span> and <span class=\"katex--inline\">0\\le \\theta &lt;360.</span> Find <span class=\"katex--inline\">\\theta.</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": 5, "problem_name": "1996 AIME Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/96_aime_p12", "prev": "/problem/96_aime_p10"}}