Complex Numbers And Quadratic Equations question 683
Question: The points $ z_1,z_2,z_3,z_4 $ in a complex plane are vertices of a parallelogram taken in order, then
Options:
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
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ z_1,z_2z_3andz_4 $ the points in complex lane be the vertices of a parallelogram taken in order. Since the diagonals of a parallelogram bisect, hence the mid points of AC and BD must coincide i.e., $ \frac{z_1+z_3}{2}=\frac{z_2+z_4}{2}\Rightarrow z_1+z_3=z_2+z_4 $
BETA
