Q. The points $z_{1},\ z_{2},\ z_{3},\ z_{4}$ in the complex plane are the vertices of a parallelogram taken in order, iff
A) $z_{1} + z_{4} = z_{2} + z_{3}\$
B) $z_{1} + z_{3} = z_{2} + z_{4}$
C) $z_{1} + z_{2} = z_{3} + z_{4}$
D) None of these
Explanation
(b)
Diagonals of parallelogram $ABCD$ are bisected each other at a point $ie$,
$\frac{z_{1} + z_{3}}{2} = \frac{z_{2} + z_{4}}{2}$
$\Rightarrow \ \ \ \ \ \ z_{1} + z_{2} = z_{2} + z_{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.