Question
Download Solution PDFThe value of ω6 + ω7 + ω5 is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Cube Roots of unity are 1, ω and ω2
Here, ω = \(\frac{{ - {\rm{\;}}1{\rm{\;}} + {\rm{\;i}}\sqrt 3 }}{2}\) and ω2 = \(\frac{{ - {\rm{\;}}1{\rm{\;}} - {\rm{\;i}}\sqrt 3 }}{2}\)
Property of cube roots of unity
- ω3 = 1
- 1 + ω + ω2 = 0
- ω3n = 1
Calculation:
ω6 + ω7 + ω5
= ω5 (ω + ω2 + 1)
= ω5 × (1 + ω + ω2)
= ω5 × 0
= 0
Last updated on Jun 11, 2025
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