if α and β are cube roots of unity prove that (1+α)(1+β)(1+α²)(1+β²) = 1
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if alpha & beta are cube roots of unity then alpha=w & beta= w^2
then
L.H.S=(1+w)(1+w^2)(1+w^2)(1+w^4)
=(1+w)(1+w^2)(1+w^2)(1+w)
=(1+w)^2×(1+w^2)^2
=(-w^2)^2×(-w)^2
=w^4×w^2
=w^6
=w^3
=1 =R.H.S
Basic*** we know that {1+w+w^2=0}
&{w^3=1}
then
L.H.S=(1+w)(1+w^2)(1+w^2)(1+w^4)
=(1+w)(1+w^2)(1+w^2)(1+w)
=(1+w)^2×(1+w^2)^2
=(-w^2)^2×(-w)^2
=w^4×w^2
=w^6
=w^3
=1 =R.H.S
Basic*** we know that {1+w+w^2=0}
&{w^3=1}
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