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Difference between revisions of "1997 AIME Problems/Problem 14"

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== Solution ==
 
== Solution ==
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The solution requires use of Euler's formula:
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<math>\displaystyle e^{i\theta}=\cos(\theta)+i\sin(\theta)</math>
  
 
== See also ==
 
== See also ==
 
* [[1997 AIME Problems]]
 
* [[1997 AIME Problems]]

Revision as of 20:03, 7 March 2007

Problem

Let $\displaystyle v$ and $\displaystyle w$ be distinct, randomly chosen roots of the equation $\displaystyle z^{1997}-1=0$. Let $\displaystyle \frac{m}{n}$ be the probability that $\displaystyle\sqrt{2+\sqrt{3}}\le\left|v+w\right|$, where $\displaystyle m$ and $\displaystyle n$ are relatively prime positive integers. Find $\displaystyle m+n$.

Solution

The solution requires use of Euler's formula: $\displaystyle e^{i\theta}=\cos(\theta)+i\sin(\theta)$

See also

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