Complex Numbers And Quadratic Equations question 314
Question: If three complex numbers are in A.P., then they lie on [IIT 1985; DCE 2001; Pb. CET 2003]
Options:
A) A circle in the complex plane
B) A straight line in the complex plane
C) A parabola in the complex plane
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ z_1,z_2,z_3 $ be three complex numbers in A.P. Then $ 2z_2=z_1+z_3 $ . Thus the complex number $ z_2 $ is the mid-point of the line joining the points $ z_1 $ and $ z_3 $ So the three points $ z_1,z_2 $ and $ z_3 $ are in a straight line.
BETA
