1997 AIME Problems/Problem 14

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: $\displaystyle e^{i\theta}=\cos(\theta)+i\sin(\theta)$

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1997 AIME Problems/Problem 14

Problem

Solution

See also