2000 AIME II Problems/Problem 9

Problem

Given that $z$ is a complex number such that $z+\frac 1z=2\cos 3^\circ$ , find the least integer that is greater than $z^{2000}+\frac 1{z^{2000}}$ .

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it. Note that if z is on the unit circle in the complex plane, then Let $z = a + bi$ and we have $z = e^i\theta$ and $\frac 1z= e^{-i\theta}$

2000 AIME II (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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2000 AIME II Problems/Problem 9

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