If ω≠1 is a cube root of unit, and 1+ω7=A+Bω. Then A, B equals

1+ω7=-ω27=-ω14 =-ω34ω2 ⇒1+ω7=-ω2 ⇒A+Bω=1+w ∴A, B=1,1

If ω≠1 is a cube root of unit, and 1+ω7=A+Bω. Then A, B equals

1+ω7=-ω27=-ω14 =-ω34ω2 ⇒1+ω7=-ω2 ⇒A+Bω=1+w ∴A, B=1,1

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If $ω (\neq 1)$ is a cube root of unit, and ${(1 + ω)}^{7} = A + Bω$ . Then $(A, B)$ equals

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$(1, 0)$

$(- 1, 1)$

$(0, 1)$

$(1, 1)$

answer is D.

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Detailed Solution

${(1 + ω)}^{7} = {(- ω^{2})}^{7} = - ω^{14} = - {(ω^{3})}^{4} ω^{2} \Rightarrow {(1 + ω)}^{7} = - ω^{2} \Rightarrow A + Bω = 1 + w ∴ (A, B) = (1, 1)$

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If ω≠1 is a cube root of unit, and 1+ω7=A+Bω. Then A, B equals

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If $ω (\neq 1)$ is a cube root of unit, and ${(1 + ω)}^{7} = A + Bω$ . Then $(A, B)$ equals