{"status": "success", "data": {"description_md": "How many nonzero complex numbers $z$ have the property that $0, z,$ and $z^3,$ when represented by points in the complex plane, are the three distinct vertices of an equilateral triangle?\n\n$\\textbf{(A) }0\\qquad\\textbf{(B) }1\\qquad\\textbf{(C) }2\\qquad\\textbf{(D) }4\\qquad\\textbf{(E) }\\text{infinitely many}$\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>How many nonzero complex numbers  <span class=\"katex--inline\">z</span>  have the property that  <span class=\"katex--inline\">0, z,</span>  and  <span class=\"katex--inline\">z^3,</span>  when represented by points in the complex plane, are the three distinct vertices of an equilateral triangle?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }0\\qquad\\textbf{(B) }1\\qquad\\textbf{(C) }2\\qquad\\textbf{(D) }4\\qquad\\textbf{(E) }\\text{infinitely many}</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": 3, "problem_name": "2019 AMC 12B Problem 17", "can_next": true, "can_prev": true, "nxt": "/problem/19_amc12B_p18", "prev": "/problem/19_amc12B_p16"}}