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If $z$ is a complex number of uni modulus and argument $θ,$ then $\arg [\frac{1 + z}{1 + \bar{z}}]$ equals

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$θ$

$- θ$

$\frac{π}{2} - θ$

$π - θ$

answer is A.

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Detailed Solution

$| z | = 1 \Rightarrow z . \bar{z} = 1 \Rightarrow \bar{z} = \frac{1}{z}$
$\frac{1 + z}{1 + \bar{z}} = \frac{1 + z}{1 + \frac{1}{z}} = z$
$\Rightarrow A r g [\frac{1 + z}{1 + \bar{z}}] = A r g (z) = θ$

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