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$Let α & β are roots of x^{2} + ω x + ω^{2} = 0, where ω is an imaginary cube root of unity and$
$z = α^{9} + i β^{9}, then value of | z | is$

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Correct option is A

Given equation is x2+ωx+ω2=0⇒x2−1+ω2x+ω2=0 ∴1+ω+ω2=0⇒ω=−1+ω2⇒α=1,β=ω2 are roots of the equation ∴z=α9+iβ9=(1)9+iω29=1+i Hence, |z|=1+1=2

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Let α & β are roots of x2+ωx+ω2=0, where ω is an imaginary cube root of unity and z=α9+iβ9, then value of |z| is

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Ready to Test Your Skills?

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$Let α & β are roots of x^{2} + ω x + ω^{2} = 0, where ω is an imaginary cube root of unity and$
$z = α^{9} + i β^{9}, then value of | z | is$