{"status": "success", "data": {"description_md": "Let $f(n) = \\left( \\frac{-1+i\\sqrt{3}}{2} \\right)^n + \\left( \\frac{-1-i\\sqrt{3}}{2} \\right)^n$, where $i = \\sqrt{-1}$. What is $f(2022)$?\n\n$\\textbf{(A) }\\ -2 \\qquad<br>\\textbf{(B) }\\ -1 \\qquad<br>\\textbf{(C) }\\ 0 \\qquad<br>\\textbf{(D) }\\ \\sqrt{3} \\qquad<br>\\textbf{(E) }\\ 2$\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>Let  <span class=\"katex--inline\">f(n) = \\left( \\frac{-1+i\\sqrt{3}}{2} \\right)^n + \\left( \\frac{-1-i\\sqrt{3}}{2} \\right)^n</span> , where  <span class=\"katex--inline\">i = \\sqrt{-1}</span> . What is  <span class=\"katex--inline\">f(2022)</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) }\\ -2 \\qquad\\textbf{(B) }\\ -1 \\qquad\\textbf{(C) }\\ 0 \\qquad\\textbf{(D) }\\ \\sqrt{3} \\qquad\\textbf{(E) }\\ 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": 3, "problem_name": "2022 AMC 12B Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12B_p12", "prev": "/problem/22_amc12B_p10"}}