z1,  z2,  z3,  z4  are distinct complex numbers representing the vertices of a quadrilateral ABCD  taken in order. If z1−z4=z2−z3  and arg (z4−z1)/(z2−z1)=π/2,  then the quadrilateral is

The first condition implies that [(z1+z3)/2]=[(z2+z4)/2],  diagonals AC  and BD  bisect each other.Hence, quadrilateral is a parallelogram.The second condition implies that the angle between AD  and AB  is 90∘ . Hence the parallelogram is a rectangle.