If α,β,γ and Δ are the roots of the equation x4−1=0, then the value of aα+bβ+cγ+dΔaγ+bΔ+cα+dβ+aγ+bΔ+cα+dβaα+bβ+cγ+dΔ is
A
3β
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B
0
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C
2γ
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D
−2
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Solution
The correct option is B−2 Clearly, α=ei0=1 β=ei2π4=i γ=ei4π4=−1 δ=ei6π4=−i So, aα+bβ+cγ+dδaγ+bδ+cα+dβ=a+bi−c−di−a−bi+c+di =−1 Similarly second expression is nothing but reciprocal of first =1−1=−1 Ans =−1−1=−2