Question
Download Solution PDFIf ω ≠ 1 is a cube root of unity, then what is (1 + ω - ω2)100 + (1 - ω + ω2)100 equal to?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
(1+ω +ω2)100+ (1-ω +ω2)100
= (– ω2 – ω2 )100 + (–ω – ω)100 {∵ 1 + ω + ω2 = 0}
= 2100(ω200 + ω100)
= 2100(ω2 + ω) (∵ ω3 = 1)
= –2100
∴ Option (d) is correct
Last updated on May 30, 2025
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