MathematicsHard53×since 2002Q3159Let S be the set of all (α,β),π<α,β<2π(\alpha, \beta), \pi<\alpha, \beta<2 \pi(α,β),π<α,β<2π, for which the complex number 1−isinα1+2isinα\frac{1-i \sin \alpha}{1+2 i \sin \alpha}1+2isinα1−isinα is purely imaginary and 1+icosβ1−2icosβ\frac{1+i \cos \beta}{1-2 i \cos \beta}1−2icosβ1+icosβ is purely real. Let Zαβ=sin2α+icos2β,(α,β)∈SZ_{\alpha \beta}=\sin 2 \alpha+i \cos 2 \beta,(\alpha, \beta) \in SZαβ=sin2α+icos2β,(α,β)∈S. Then ∑(α,β)∈S(iZαβ+1iZˉαβ)\sum\limits_{(\alpha, \beta) \in S}\left(i Z_{\alpha \beta}+\frac{1}{i \bar{Z}_{\alpha \beta}}\right)(α,β)∈S∑(iZαβ+iZˉαβ1) is equal to :A3B3 iC1D2 −-− iCheck answerSkip