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>.
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== See also ==
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{{AIME box|year=2012|n=I|num-b=5|num-a=7}}

Revision as of 20:47, 16 March 2012

Problem 6

Let $z$ and $w$ be complex numbers such that $z^{13} = w$ and $w^{11} = z$. If the imaginary part of $z$ can be written as $\sin {\frac{m\pi}{n}}$, where $m$ and $n$ are relatively prime positive integers, find $n$.

See also

2012 AIME I (ProblemsAnswer KeyResources)
Preceded by
Problem 5
Followed by
Problem 7
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All AIME Problems and Solutions
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