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Question
If 1,ω,ω2 are the cube roots of unity, then the value of (3+ω)(3+ω2)(3+ω10)(3+ω11) is
If 1,ω,ω2 are the cube roots of unity, then the value of (3+ω)(3+ω2)(3+ω10)(3+ω11) is
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Solution
The correct option is A 49
we know,
(x3−1)=(x−1)(x−ω)(x−ω2)
Substituting x=−3
(−28)=(−3−1)(−3−ω)(−3−ω2)
⇒(3+ω)(3+ω2)=7
Hence,
(3+ω)(3+ω2)(3+ω10)(3+ω11)=(3+ω)2(3+ω2)2=49
we know,
(x3−1)=(x−1)(x−ω)(x−ω2)
Substituting x=−3
(−28)=(−3−1)(−3−ω)(−3−ω2)
⇒(3+ω)(3+ω2)=7
Hence,
(3+ω)(3+ω2)(3+ω10)(3+ω11)
=(3+ω)2(3+ω2)2
=49
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