Two unit squares ,, with centers M, N are situated in the plane so that . Two sides of are parallel to the line MN, and one of the diagonals of lies on MN. Find the locus of the midpoint of XY as X, Y vary over the interior of , respectively.
(1997 Bulgarian mathematical olympiad)
Introduce complex numbers with , . Then, the locus is the set of points of the form , where , , and , . The result is an octagon with vertices , , and so on.
Ref: Complex Numbers from A to …Z by Titu Andreescu and Dorin Andrica.
Thanks Prof. Andreescu !