IIT-JEE 1983Question 1
The points $z_1,z_2,z_3,z_4$ in the complex plane are the vertices of a parallelogram taken in order if and only if
Complex Numbers
Solution
$z_1z_2z_3z_4$ is a parallelogram iff its diagonals bisect each other: $\frac{z_1+z_3}2=\frac{z_2+z_4}2$, i.e. $z_1+z_3=z_2+z_4$.