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Counting vertices

Source: Czech and Slovak Olympiad 1955, National Round, Problem 3

August 14, 2022
complex numbersgeometryregular polygon

Problem Statement

In the complex plane consider the unit circle with the origin as its center. Furthermore, consider inscribed regular 17-gon with one of its vertices being 1+0i.1+0i. How many of its vertices lie in the (open) unit disc centered in 3/2(1+i)\sqrt{3/2}(1+i)?
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