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
?
z=a+bi
a
b
z=a-bi
z$)
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