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State true or false for the following : The points representing the complex number z for which $\;|z+1| < |z-1|\;$ lies in the interior of a circle

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

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Answer : False
Explanation :
False , because $\;|x+iy+1| < |x+iy-1|\;$
$|(x+1)^{2} + y^{2}| < |(x-1)^{2} + y^{2}| $
Which gives $\; 4x < 0$
answered Apr 18, 2014 by yamini.v
 

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