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:
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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