{"status": "success", "data": {"description_md": "Let $f : \\mathbb{C} \\to \\mathbb{C}$ be defined by $f(z) = z^2 + iz + 1$. How many complex numbers $z$ are there such that $\\text{Im}(z) > 0$ and both the real and the imaginary parts of $f(z)$ are integers with absolute value at most $10$?\n\n$\\textbf{(A)} \\ 399 \\qquad \\textbf{(B)} \\ 401 \\qquad \\textbf{(C)} \\ 413 \\qquad \\textbf{(D)} \\ 431 \\qquad \\textbf{(E)} \\ 441$\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 : \\mathbb{C} \\to \\mathbb{C}</span>  be defined by  <span class=\"katex--inline\">f(z) = z^2 + iz + 1</span> . How many complex numbers  <span class=\"katex--inline\">z</span>  are there such that  <span class=\"katex--inline\">\\text{Im}(z) &gt; 0</span>  and both the real and the imaginary parts of  <span class=\"katex--inline\">f(z)</span>  are integers with absolute value at most  <span class=\"katex--inline\">10</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)} \\ 399 \\qquad \\textbf{(B)} \\ 401 \\qquad \\textbf{(C)} \\ 413 \\qquad \\textbf{(D)} \\ 431 \\qquad \\textbf{(E)} \\ 441</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": "2013 AMC 12A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/13_amc12A_p24"}}