2018 AMC 12A Problems/Problem 22
Problem
The solutions to the equations and
where
form the vertices of a parallelogram in the complex plane. The area of this parallelogram can be written in the form
where
and
are positive integers and neither
nor
is divisible by the square of any prime number. What is
Solution
The roots are (easily derivable by using DeMoivre and half-angle). From there, shoelace on
and multiplying by
gives the area of
, so the answer is
. (trumpeter)
See Also
2018 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 21 |
Followed by Problem 23 |
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