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If $z_1+z_2+z_3=0$ and $\mid z_1\mid=\mid z_2\mid=\mid z_3\mid=1$ then value of $z_1^2+z_2^2+z_3^2$ equals

$\begin{array}{1 1}(A)-1 \\ (B) 0 \\ (C) 1 \\(D) 3 \end{array}$

1 Answer

$z_1^2+z_2^2+z_3^2=(z_1+z_2+z_3)^2-2(z_1z_2+z_2z_3+z_1z_3)$
$\Rightarrow 0-2z_1z_2z_3(\large\frac{1}{z_1}+\frac{1}{z_2}+\frac{1}{z_3})$
$\Rightarrow -2z_1z_2z_3(\overline {z_1}+\overline {z_2}+\overline {z_3})$
$\Rightarrow 0$
Hence (B) is the correct answer.
answered Apr 9, 2014 by sreemathi.v
 

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