Difference between revisions of "2023 AMC 12A Problems/Problem 16"
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| − | + | ==Problem== | |
| + | Consider the set of complex numbers <math>z</math> satisfying <math>|1+z+z^{2}|=4</math>. The maximum value of the imaginary part of <math>z</math> can be written in the form <math>\tfrac{\sqrt{m}}{n}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers. What is <math>m+n</math>? | ||
| − | - | + | <math>\textbf{(A)}~20\qquad\textbf{(B)}~21\qquad\textbf{(C)}~22\qquad\textbf{(D)}~23\qquad\textbf{(E)}~24</math> |
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| + | ==Solution== | ||
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| + | |||
| + | ==See Also== | ||
| + | {{AMC12 box|year=2023|ab=A|num-b=16|num-a=17}} | ||
| + | {{MAA Notice}} | ||
Revision as of 22:51, 9 November 2023
Problem
Consider the set of complex numbers 
satisfying 
. The maximum value of the imaginary part of can be written in the form 
, where 
and 
are relatively prime positive integers. What is 
?
Solution
See Also
| 2023 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 16 |
Followed by Problem 17 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
