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If $α (\neq 1)$ is a fifth root of unity and $β (\neq 1)$ is a fourth root of unity then $z = (1 + α) (1 + β) (1 + α^{2}) (1 + β^{2}) (1 + α^{3}) (1 + β^{3})$ equals

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Correct option is D

As β≠1s a fourth root of unity,β4=1⇒(1−β)1+β+β2+β3=0as, β≠1,1+β+β2(1+β)=0⇒(1+β)1+β2=0∴z=0

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If α(≠1) is a fifth root of unity and β≠1 is a fourth root of unity then z=(1+α)(1+β)1+α21+β21+α31+β3 equals

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If $α (\neq 1)$ is a fifth root of unity and $β (\neq 1)$ is a fourth root of unity then $z = (1 + α) (1 + β) (1 + α^{2}) (1 + β^{2}) (1 + α^{3}) (1 + β^{3})$ equals