The points z1,z2,z3,z4 in the complex plane are the vertices of a parallelogram taken in order, if and only if:
z1+z4=z2+z3
z1+z3=z2+z4
z1+z2=z3+z4
None of these
Diagonals of a parallelogram are bisected each other at a point
i.e., z1+z32=z2+z42
⇒ z1+z3=z2+z4 .