2011 AMC 12B Problems/Problem 24
Problem
Let . What is the minimum perimeter amont all the -sided polygons in the complex plane whose vertices are precisely the zeros of ?
Solution
Answer: (B)
First of all, we need to find all such that
So or
or
Now we have a solution at if we look at them in polar coordinate, further more, the 8-gon is symmetric (it is a regular octagon) . So we only need to find the side length of one and multiply by .
So answer distance from to
Side length
Hence, answer is .
See also
2011 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 23 |
Followed by Problem 25 |
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All AMC 12 Problems and Solutions |