{"status": "success", "data": {"description_md": "How many complex numbers satisfy the equation $z^{5}=\\overline{z}$, where $\\overline{z}$ is the conjugate of the complex number $z$?\n\n$\\textbf{(A)}~2\\qquad\\textbf{(B)}~3\\qquad\\textbf{(C)}~5\\qquad\\textbf{(D)}~6\\qquad\\textbf{(E)}~7$\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 complex numbers satisfy the equation  <span class=\"katex--inline\">z^{5}=\\overline{z}</span> , where  <span class=\"katex--inline\">\\overline{z}</span>  is the conjugate of the complex number  <span class=\"katex--inline\">z</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}~2\\qquad\\textbf{(B)}~3\\qquad\\textbf{(C)}~5\\qquad\\textbf{(D)}~6\\qquad\\textbf{(E)}~7</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": "2023 AMC 12A Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/23_amc12A_p15", "prev": "/problem/23_amc12A_p13"}}