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State true or false for the following : If three complex numbers $\;z_{1} , z_{2}\;$ and $\;z_{3}\;$ are in A.P. then they lie on a circle in the complex plane .

$(a)\;True\qquad(b)\;false$

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Answer : False
Explanation :
False , because if $\;z_{1} , z_{2}\;$ and $\;z_{3}\;$ are in A.P. then $\;z_{1} = \large\frac{z_{1}+z_{3}}{2}\;$ => $\;z_{2}\;$ is the mid point of $\;z_{1}\;$ and $\;z_{3}\;$ => which implies that the points $\;z_{1} , z_{2} , z_{3}\;$ are collinear
answered Apr 18, 2014 by yamini.v
 

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