{"status": "success", "data": {"description_md": "Let $z = a + bi$ be the complex number with $|z| = 5$ and $b > 0$ such that the distance between $(1 + 2i)z^3$ and $z^5$ is maximized, and let $z^4 = c + di$.<br>Find $c+d$.\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\">z = a + bi</span> be the complex number with <span class=\"katex--inline\">|z| = 5</span> and <span class=\"katex--inline\">b &gt; 0</span> such that the distance between <span class=\"katex--inline\">(1 + 2i)z^3</span> and <span class=\"katex--inline\">z^5</span> is maximized, and let <span class=\"katex--inline\">z^4 = c + di</span>.<br/>Find <span class=\"katex--inline\">c+d</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 6", "can_next": true, "can_prev": true, "nxt": "/problem/12_aime_II_p07", "prev": "/problem/12_aime_II_p05"}}