1992 AIME Problem 10

Consider the region A in the complex plane that consists of all points z such that both z / 40 and 40 / \bar{z} have real and imaginary parts between 0 and 1 inclusive. What is the integer that is nearest the area of A? (If z=x+i y with x and y real, then \bar{z}=x-i y is the conjugate of z.)