For any complex number \( w=c+i d \), let \( \arg (w) \in(-\pi, \pi] \), P where \( i=\sqrt{-1} ...

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For any complex number w = c + id, arg(w)=(-Π,Π] let , where . Let α and β be real numbers such that For any complex number w = c + id, arg(w)=(-Π,Π] let , where . Let α and β be real numbers such that
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If z,w be complex numbers such that |zw|=1,arg z - arg w=3 pi/2.Find arg(1-2 \bar z w)/(1+3\bar z w) If z,w be complex numbers such that |zw|=1,arg z - arg w=3 pi/2.Find arg(1-2 \bar z w)/(1+3\bar z w)
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if z and w are two complex numbers such that ∣zw∣=1 and arg(z)-arg(w)=π/2, then show that z ̅w=-i if z and w are two complex numbers such that ∣zw∣=1 and arg(z)-arg(w)=π/2, then show that z ̅w=-i