Q. If $z_{,},\ z_{2}$ and $z_{3}$ are any three complex numbers, then the fourth vertex of the parallelogram whose three vertices are $z_{1},\ z_{2}$ and $z_{3}$ taken in order is
A) $z_{1} - z_{2} + z_{3}$
B) $z_{1} + z_{2} + z_{3}$
C) $\frac{1}{3}(z_{1} - z_{2} + z_{3})$
D) $\frac{1}{3}(z_{1} + z_{2} - z_{3})$
Explanation
(a)
Let $z$ be the fourth vertex of parallelogram, then
$\frac{z_{1} + z_{3}}{2} = \frac{z_{2} + z}{2}\ \ \Rightarrow \ \ \ z = z_{1} + z_{3} - z_{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.