Complex number $z_{1}$ , $z_{2}$ and $z_{3}$ in A.P, then they

lie on eclipse

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lie on a parabola

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lie on line

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lie on circle

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Solution

The correct option is C lie on line
$z_{1} + z_{3} = 2 z_{2}$
$z_{2} = \frac{z_{1} + z_{3}}{2}$
Therefore $z_{1}, z_{2}, z_{3}$ lie on a line.

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