If $z_1,z_2,z_3,z_4$ are the four complex numbers represented by the vertices of a quadrilateral taken in order such that $z_1-z_4=z_2-z_3$ and $amp\frac{z_4-z_1}{z_2-z_1}=\frac{\pi }{2}$ then the quadrilateral is a

$z_1,z_2,z_3,z_4$ are the four complex numbers 

$z_1-z_4=z_2-z_3$

$amp\frac{z_4-z_1}{z_2-z_1}=\frac{\pi }{2}$

We have 

$z_1-z_4=z_2-z_3$    or     $\frac{z_1+z_3}{2}=\frac{z_2+z_4}{2}$

that is 

The diagonal bisect each other 

Therefore it is a parallelogram 

Also $amp\frac{z_4-z_1}{z_2-z_1}=\frac{\pi }{2}$

angle as $z_1$ is a right angle 

Hence it is a rectangle and a cyclic quadrilateral 

Options c and d are correct