QJEEM13Ma8209: JEE Main 2013 Mathematics - Class 11 JEEM13Ma8209 Solution: If z is a complex number of unit modulus and argument θ , then…

Question

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If z is a complex number of unit modulus and argument

θ

, then arg

(\frac{1 + z}{1 + \overset{―}{z}})

equals :

Accepted Answer

Given

| z | = 1, \arg z = θ

As we know,

\vec{z} = \frac{1}{z}

∴

\arg (\frac{1 + z}{1 + \vec{z}}) = \arg (\frac{1 + z}{1 + \frac{1}{z}})

= \arg (z) = θ .

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