1992 AIME Problems/Problem 10
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Problem
Consider the region in the complex plane that consists of all points
such that both
and
have real and imaginary parts between
and
, inclusive. What is the integer that is nearest the area of
?
Solution
Let . Since
we have the inequality
which is a square of side length
.
Also, so we have
, which leads to:
We graph them:
![AIME 1992 Solution 10.png](https://wiki-images.artofproblemsolving.com//1/1b/AIME_1992_Solution_10.png)
We want the area outside the two circles but inside the square. Doing a little geometry, the area of the intersection of those three graphs is
See also
1992 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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