1992 AIME Problems/Problem 10
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:
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 | |
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All AIME Problems and Solutions |