Difference between revisions of "2012 AIME I Problems/Problem 6"
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| + | ==Problem 6== | ||
Let <math>z</math> and <math>w</math> be complex numbers such that <math>z^{13} = w</math> and <math>w^{11} = z</math>. If the imaginary part of <math>z</math> can be written as <math> \sin {\frac{m\pi}{n}}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers, find <math>n</math>. | Let <math>z</math> and <math>w</math> be complex numbers such that <math>z^{13} = w</math> and <math>w^{11} = z</math>. If the imaginary part of <math>z</math> can be written as <math> \sin {\frac{m\pi}{n}}</math>, where <math>m</math> and <math>n</math> are relatively prime positive integers, find <math>n</math>. | ||
| + | |||
| + | == See also == | ||
| + | {{AIME box|year=2012|n=I|num-b=5|num-a=7}} | ||
Revision as of 20:47, 16 March 2012
Problem 6
Let 
and 
be complex numbers such that 
and 
. If the imaginary part of can be written as 
, where 
and 
are relatively prime positive integers, find .
See also
| 2012 AIME I (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
