Question

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

• A. straight line
• B. circle
• C. parabola

Answer 1

The correct option is A straight line

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.