If z and ω are two complex numbers such that | zω | = 1 and arg (z) - arg (ω) = (3π)/2, then arg ((1 - 2 z ω)/(1 + 3 z ω)) is: (Here arg(z) denotes the principal argument of complex number z)

Complex Numbers and Quadratic Equations: JEE Main 2021 Mathematics question

JEE Main 2021 · 20 Jul, Morning shift · Q3213

JEE Main 202120 Jul, Morning shiftMathematicsMediumComplex Numbers and Quadratic Equations264× since 2002

If z and

\omega

are two complex numbers such that

\left| {z\omega } \right| = 1

and

\arg (z) - \arg (\omega ) = {{3\pi } \over 2}

, then

\arg \left( {{{1 - 2\overline z \omega } \over {1 + 3\overline z \omega }}} \right)

is : (Here arg(z) denotes the principal argument of complex number z)