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If ω is a cube root of unity then the value of (1−ω8)(1−ω4)(1−ω2)(1−ω) is ___
- a)1
- b)9
- c)0
- d)6
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
If ω is a cube root of unity then the value of(1−ω8)...
We know that 1+ω+ω2=0 and ω3 =1 then
(1−ω8)(1−ω4)(1−ω2)(1−ω) = (1−ω2)(1−ω)(1−ω2)(1−ω)
= (1−ω2−ω+ω3)(1−ω2−ω+ω3)
= (2−(ω+ω2))(2−(ω+ω2))
= (2−(−1))(2−(−1)) = 9
(1−ω8)(1−ω4)(1−ω2)(1−ω) = (1−ω2)(1−ω)(1−ω2)(1−ω)
= (1−ω2−ω+ω3)(1−ω2−ω+ω3)
= (2−(ω+ω2))(2−(ω+ω2))
= (2−(−1))(2−(−1)) = 9
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If ω is a cube root of unity then the value of(1−ω8)(1−ω4)(1−ω2)(1−ω) is ___a)1b)9c)0d)6Correct answer is option 'B'. Can you explain this answer?
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If ω is a cube root of unity then the value of(1−ω8)(1−ω4)(1−ω2)(1−ω) is ___a)1b)9c)0d)6Correct answer is option 'B'. Can you explain this answer? for Defence 2025 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If ω is a cube root of unity then the value of(1−ω8)(1−ω4)(1−ω2)(1−ω) is ___a)1b)9c)0d)6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If ω is a cube root of unity then the value of(1−ω8)(1−ω4)(1−ω2)(1−ω) is ___a)1b)9c)0d)6Correct answer is option 'B'. Can you explain this answer?.
If ω is a cube root of unity then the value of(1−ω8)(1−ω4)(1−ω2)(1−ω) is ___a)1b)9c)0d)6Correct answer is option 'B'. Can you explain this answer? for Defence 2025 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about If ω is a cube root of unity then the value of(1−ω8)(1−ω4)(1−ω2)(1−ω) is ___a)1b)9c)0d)6Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Defence 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If ω is a cube root of unity then the value of(1−ω8)(1−ω4)(1−ω2)(1−ω) is ___a)1b)9c)0d)6Correct answer is option 'B'. Can you explain this answer?.
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