`z_1, z_2, z_3,z_4` are distinct complex numbers representing the vertices of a quadrilateral `A B C D` taken in order. If `z_1-z_4=z_2-z_3 and "arg"[(z_4-z_1)//(z_2-z_1)]=pi//2` , the quadrilateral is

Options

A. rectangle
B. rhombus
C. square
D. trapezium

Answer

A

Explanation

The first condition implies that `(z_(1) + z_(3)) //2= (z_(2) + z_(4))//2`, i.e., diagonal 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.