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 2$z_2$=$z_1$+$z_3$.

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.