If z is a complex number of unit modulus and argument θ , then arg ( 1 + z 1 + ¯ z ) is equal to Options: A . &nbsp−θ B . &nbspπ2−θ C . &nbspθ D . &nbspπ−θ

Answer: Option C : C Given, | z 1 | = 1 , arg z = θ ∴ z = e − i θ But ¯ ¯ ¯ z = 1 z ∴ a r g ( 1 + z 1 + 1 z ) = a r g ( z ) = θ

If z is a complex number of unit modulus and argument θ, then arg(1+z1+&#x

Question

If z is a complex number of unit modulus and argument

θ

, then arg

(\frac{1 + z}{1 + ¯ z})

is equal to

Options:

A . −θ

B . π2−θ

C . θ

D . π−θ

Answer: Option C
:
C
Given,

| z_{1} | = 1

, arg

z = θ ∴ z = e^{- i θ}

But

¯ ¯ ¯ z = \frac{1}{z} ∴ a r g (\frac{1 + z}{1 + \frac{1}{z}}) = a r g (z) = θ

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