{"status": "success", "data": {"description_md": "The solutions of the equation $z^4+4z^3i-6z^2-4zi-i=0$ are the vertices of a convex polygon in the complex plane. What is the area of the polygon?\n\n$\\mathrm{(A)}\\ 2^{\\frac{5}{8}}\\qquad\\mathrm{(B)}\\ 2^{\\frac{3}{4}}\\qquad\\mathrm{(C)}\\ 2\\qquad\\mathrm{(D)}\\ 2^{\\frac{5}{4}}\\qquad\\mathrm{(E)}\\ 2^{\\frac{3}{2}}$\n___\nFull 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 solutions of the equation  <span class=\"katex--inline\">z^4+4z^3i-6z^2-4zi-i=0</span>  are the vertices of a convex polygon in the complex plane. What is the area of the polygon?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 2^{\\frac{5}{8}}\\qquad\\mathrm{(B)}\\ 2^{\\frac{3}{4}}\\qquad\\mathrm{(C)}\\ 2\\qquad\\mathrm{(D)}\\ 2^{\\frac{5}{4}}\\qquad\\mathrm{(E)}\\ 2^{\\frac{3}{2}}</span> </p>&#10;<hr><p>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": "2008 AMC 12A Problem 23", "can_next": true, "can_prev": true, "nxt": "/problem/08_amc12A_p24", "prev": "/problem/08_amc12A_p22"}}