Difference between revisions of "2019 AMC 12B Problems/Problem 24"
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Revision as of 17:48, 14 February 2019
Problem
Let Let
denote all points in the complex plane of the form
where
and
What is the area of
?
Solution
Let be the third root of unity. We wish to find the span of
for reals
.
Note that if
, then
forms the same point as
. Therefore, assume that at least one of them is equal to
. If only one of them is equal to zero, we can form an equilateral triangle with the remaining two, of side length
. Similarly for if two are equal to zero. So the area of the six equilateral triangles is
Here is a diagram:
-programjames1
See Also
2019 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 23 |
Followed by Problem 25 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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