Question

If the complex numbers $z_1,z_2,z_3$ are in A.P., then they lie on a

• A. circle
• B. parabola
• C. line
• D. ellipse

Answer 1

Answer: (C)

line

Let $z_1,z_2,z_3$ be affixes of points $A,B,C$ respectively.

Since $z_1,z_2,z_3$ are in A.P., therefore

$2z_2=z_1+z_2\Rightarrow z_2=\frac{z_1+z_3}{2}$

$\Rightarrow B$ is mid point of the line $AC$

$\Rightarrow A,B,C$ are collinear

$\therefore z_1,z_2,z_3$ lie on line.