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Q.

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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a

α

b

β

c

αβ

d

0

answer is D.

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Detailed Solution

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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