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Question
If ω represents a complex cube root of unity, then (3−ω)(3−ω2)(3−ω4)(3−ω8)=
If ω represents a complex cube root of unity, then (3−ω)(3−ω2)(3−ω4)(3−ω8)=
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Solution
The correct option is C 169
(3−w)(3−w2)(3−w4)(3−w8)
=(3−w)(3−w2)(3−w3w)(3−w6.w2)
=(3−w)(3−w2)(3−w)(3−w2) since w3n=1
=[(3−w)(3−w2)]2
=(9−3(w+w2)+w3)2
=(10−3(−1))2
=(13)2
=169.
(3−w)(3−w2)(3−w4)(3−w8)
=(3−w)(3−w2)(3−w3w)(3−w6.w2)
=(3−w)(3−w2)(3−w)(3−w2) since w3n=1
=[(3−w)(3−w2)]2
=(9−3(w+w2)+w3)2
=(10−3(−1))2
=(13)2
=169.
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