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Complex Numbers question

2021 · 20 Jul · Shift 1 · Q27
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  5. /2021 · 20 Jul · Shift 1 · Q27

Complex Numbers question

2021 · 20 Jul · Shift 1 · Q27

JEE MainMathematicsComplex NumbersMCQ+4 / −1
If z and ω\omegaω are two complex numbers such that ∣zω∣=1\left| {z\omega } \right| = 1∣zω∣=1 and arg⁡(z)−arg⁡(ω)=3π2\arg (z) - \arg (\omega ) = {{3\pi } \over 2}arg(z)−arg(ω)=23π​, then arg⁡(1−2z‾ω1+3z‾ω)\arg \left( {{{1 - 2\overline z \omega } \over {1 + 3\overline z \omega }}} \right)arg(1+3zω1−2zω​) is : (Here arg(z) denotes the principal argument of complex number z)
  1. A
    π4{\pi \over 4}4π​
  2. B
    −3π4- {{3\pi } \over 4}−43π​
  3. C
    −π4- {\pi \over 4}−4π​
  4. D
    3π4{{3\pi } \over 4}43π​
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