If three complex numbers are in A.P., then they lie on a circle in the complex plane. If this is true enter 1, else enter 0.

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Solution

given that $2 z_{2} = z_{1} + z_{3}$
$\Rightarrow \frac{z_{2} - z_{3}}{z_{2} - z_{1}} = - 1$
$a r g (\frac{z_{2} - z_{3}}{z_{2} - z_{1}}) = a r g (- 1) = 0$
Therefore, $z_{1}$ , $z_{2}$ & $z_{3}$ are collinear.
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