If ω (  = 1 ) is a cube root of unity, and ( 1 + ω ) 7 = A + B ω . Then ( A , B ) equals

1 + ω = − ω 2 ( 1 + ω ) 7 = ( − ω 2 ) 7 = − ω 14 = − ω 2 = 1 + ω = A + B ω ⇒ ( A , B ) = ( 1 , 1 )

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MathematicsComplex NumberCube Root of UnityMedium2 minPYQ_2011

MathematicsMediumsingle choice

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

Answer:

Solution:

$1 + ω = - ω^{2}$ $(1 + ω)^{7} = (- ω^{2})^{7} = - ω^{14} = - ω^{2} = 1 + ω = A + B ω \Rightarrow (A, B) = (1, 1)$

Stream:JEESubject:MathematicsTopic:Complex NumberSubtopic:Cube Root of Unity

⏱ 2mℹ️ Source: PYQ_2011

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