1992 AIME Problems/Problem 10

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Problem

Consider the region $A^{}_{}$ in the complex plane that consists of all points $z$ such that both $\frac{z^{}_{}}{40}$ and $\frac{40^{}_{}}{\overline{z}}$ have real and imaginary parts between $0^{}_{}$ and $1^{}_{}$, inclusive. What is the integer that is nearest the area of $A^{}_{}$?

Solution

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See also