1.e) (a+bω+cω²)/(aω+bω²+c) + (a+bω+cω²)/(aω²+b+cω) = –1 If ω be complex cube root unity show that :

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1.a) (1+ω–ω²)³ –(1–ω+ω²)³ = 0 . If ω be complex cube root of unity, show that (1+w–w²)³–(1–w+w²)³=0 1.a) (1+ω–ω²)³ –(1–ω+ω²)³ = 0 . If ω be complex cube root of unity, show that (1+w–w²)³–(1–w+w²)³=0
The value of (a+bω+cω^2)/(c+aω+bω^2 ) where ω is a complex cube root of unity, is The value of (a+bω+cω^2)/(c+aω+bω^2 ) where ω is a complex cube root of unity, is
4.i) show that: x + y + z = 0 If x=a+b, y=aω+bω², z=aω²+bω. complex cube root of unity Class 12 NEB 4.i) show that: x + y + z = 0 If x=a+b, y=aω+bω², z=aω²+bω. complex cube root of unity Class 12 NEB
4.ii) show that: xyz = a³ + b³ If x=a+b, y=aω+bω², z=aω²+bω. complex cube root unity xyz= a^3 + b^3 4.ii) show that: xyz = a³ + b³ If x=a+b, y=aω+bω², z=aω²+bω. complex cube root unity xyz= a^3 + b^3
1.d) (1–ω)(1–ω²)(1–ω⁴)(1–ω⁸) = 9 If ω be complex cube root unity show that (1–w)(1–w²)(1–w⁴)(1–w⁸)=9 1.d) (1–ω)(1–ω²)(1–ω⁴)(1–ω⁸) = 9 If ω be complex cube root unity show that (1–w)(1–w²)(1–w⁴)(1–w⁸)=9
1.c) (1–ω+ω²)⁴ (1+ω–ω²)⁴ =256. If ω be cube root unity, show that (1–w+w²)⁴ (1+w–w²)⁴ = 256 Class 12 1.c) (1–ω+ω²)⁴ (1+ω–ω²)⁴ =256. If ω be cube root unity, show that (1–w+w²)⁴ (1+w–w²)⁴ = 256 Class 12
a, b, c are integers, not all simultaneously equal and ω is cube root of unity (ω ≠...| Doubtify JEE a, b, c are integers, not all simultaneously equal and ω is cube root of unity (ω ≠...| Doubtify JEE
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