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If $\omega=\large\frac{z-\perp}{z+1}$$\quad (z\neq -\perp)$ and $\mid z\mid =\perp$ then $Re(\omega)$ equals

$\begin{array}{1 1} \frac{\sqrt 2 }{|z+1|^2 } \\ \bigg|\frac{z}{z+1} \bigg| \frac{1}{|z+1|^2} \\ zero \\ None\;of\;these \end{array}$

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$\mid z\mid=1\Rightarrow z\overline{z}=1$
$\Rightarrow \large\frac{z-1}{z+1}+\frac{\overline {z}-1}{\overline {z}+1}$
$\Rightarrow \large\frac{z\overline{z}+z-\overline{z}-1+z\overline{z}-z+\overline{z}-1}{(z+1)(\overline{z}+1)}$$=0$
$\Rightarrow \large\frac{2z\overline{z}-2}{(z+1)(\overline{z}+1)}$$=0$
$\Rightarrow Re(\omega)=0$
Hence (C) is the correct answer.
answered Apr 9, 2014 by sreemathi.v
edited May 29, 2014 by rohanmaheshwari0831_1

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