Question

If three complex numbers are in A.P., then they lie on

• 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

Answer 1

The correct option is B A straight line in the complex plane

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 $z_i$ and $z_3$
So the three points $z_1,z_2$ and $z_3$ are in a straight line.