{"status": "success", "data": {"description_md": "A function $f$ is defined by $f(z) = i\\overline{z}$, where $i=\\sqrt{-1}$ and $\\overline{z}$ is the [[complex conjugate]] of $z$. How many values of $z$ satisfy both $|z| = 5$ and $f(z) = z$?\n\n$\\mathrm{(A)}\\ 0\\qquad\\mathrm{(B)}\\ 1\\qquad\\mathrm{(C)}\\ 2 \\qquad\\mathrm{(D)}\\ 4\\qquad\\mathrm{(E)}\\ 8$\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>A function <span class=\"katex--inline\">f</span> is defined by <span class=\"katex--inline\">f(z) = i\\overline{z}</span>, where <span class=\"katex--inline\">i=\\sqrt{-1}</span> and <span class=\"katex--inline\">\\overline{z}</span> is the [[complex conjugate]] of <span class=\"katex--inline\">z</span>. How many values of <span class=\"katex--inline\">z</span> satisfy both <span class=\"katex--inline\">|z| = 5</span> and <span class=\"katex--inline\">f(z) = z</span>?</p>&#10;<p><span class=\"katex--inline\">\\mathrm{(A)}\\ 0\\qquad\\mathrm{(B)}\\ 1\\qquad\\mathrm{(C)}\\ 2 \\qquad\\mathrm{(D)}\\ 4\\qquad\\mathrm{(E)}\\ 8</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2004 AMC 12B Problem 16", "can_next": true, "can_prev": true, "nxt": "/problem/04_amc12B_p17", "prev": "/problem/04_amc12B_p15"}}