If z is a complex number of unit modulus and argument θ, then arg \left(\right. \frac{1 + z}{1 + \bar{z}} \left.\right) equals :

Engineering

Mathematics

Conjugate Modulus and Argument of a Complex Number

Question

If z is a complex number of unit modulus and argument θ, then arg $(\frac{1 + z}{1 + \bar{z}})$ equals :

$- θ$

$\frac{π}{2} - θ$

$π - θ$

$θ$

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$| z | = 1 \Rightarrow | z |^{2} = 1 \Rightarrow z \bar{z} = 1$

$\arg (\frac{1 + z}{1 + \bar{z}}) = \arg (\frac{1 + z}{1 + \frac{1}{z}}) = \arg (z) = θ$