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

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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^34.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.iii show that: x³ + y³ + z³ = 3(a³ + b³) If x=a+b, y=aω+bω², z=aω²+bω. complex cube root unity NEB4.iii show that: x³ + y³ + z³ = 3(a³ + b³) If x=a+b, y=aω+bω², z=aω²+bω. complex cube root unity NEB
1.e) (a+bω+cω²)/(aω+bω²+c) + (a+bω+cω²)/(aω²+b+cω) = –1 If ω be complex cube root unity show that :1.e) (a+bω+cω²)/(aω+bω²+c) + (a+bω+cω²)/(aω²+b+cω) = –1 If ω be complex cube root unity show that :
2.b) If α and β complex cube root of unity, prove that: α⁴ + β⁴ + α‐¹β-¹ = 0. α^4 +β^4 + α^-1 β^-1=02.b) If α and β complex cube root of unity, prove that: α⁴ + β⁴ + α‐¹β-¹ = 0. α^4 +β^4 + α^-1 β^-1=0
BCS 012 TEE June 2021 Q4b solution If x=a+b, y=aw+bw2, z=aw2+bw (where w !=1), show that xyz=a3+b3BCS 012 TEE June 2021 Q4b solution If x=a+b, y=aw+bw2, z=aw2+bw (where w !=1), show that xyz=a3+b3
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)=91.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
2.a) If α= 1/2 (–1+ √–3) and β= 1/2 (–1– √–3), show that α⁴ + α²β² + β⁴ = 0 Cube root of Unity. NEB2.a) If α= 1/2 (–1+ √–3) and β= 1/2 (–1– √–3), show that α⁴ + α²β² + β⁴ = 0 Cube root of Unity. NEB
15.23 | Complex Numbers | Cube Roots Of Unity15.23 | Complex Numbers | Cube Roots Of Unity