If z and ω are two complex numbers such that |zω|=1 and arg(z)−arg(ω)=3π2, then arg(1−2¯¯¯zω1+3¯¯¯zω) is
(Here arg(z) denotes the principal argument of complex number z )
A
3π4
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B
−3π4
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C
π4
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D
−π4
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Solution
The correct option is B−3π4 z=reiθ∴ω=1rei(θ−3π/2) 1−2¯¯¯zω1+3¯¯¯zω=1−2e−iθ⋅ei(−3π/2+θ)1+3e−iθ⋅ei(−3π/2+θ)=1−2i1+3i