R is the region in the complex plane that consists of all points z such that each of z/40 and 40/z have real and imaginary parts between 0 and 1 inclusively.

Find the area of R.

Express z/40 in polar form, call it (r,theta). For z/40 to be in the square, 0<r<=sqrt(2) and 0<=theta<=pi/2. (These bounnds are necessary but not sufficient.)

40/z is the reciprocal of z/40. Then 40/z in polar form equals (1/r, -theta). For 40/z to also be in the square, 0<1/r<=sqrt(2) and 0<=-theta<=pi/2.

The two theta ranges intersect at one value: theta=0. That reduces the possible values of z/40 and 40/z to the real axis. With this restriction then 0<{40/z and z/40}<1. A positive number and its reciprocal can only be in that range if the number is 1. Then 40/z=z/40=1.

Therefore the set of all z is the single real number z=40.