(i) If `alpha`,`beta` be the imaginary cube root of unity, then show t – InterviewSolution

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1.	(i) If `alpha`,`beta` be the imaginary cube root of unity, then show that `alpha^4+beta^4+alpha^-1beta^-1=0`
Answer» `1,w,w^2` `alpha,beta` `alpha=-1/2-sqrt3/2i` `beta=-1/2+sqrt3/2i` `alpha*beta=(-1/2-sqrt3/2i)(-1/2+sqrt3/2i)` `=(-1/2)^2-(sqrt3/2i)^2` `=1/4-3/4i^2` `=1` LHS=`(alphabeta(alpha^4+beta^4)+1)/(alphabeta)` `=(1(alpha+beta)+1)/1` `=1+alpha+beta` =0=RHS

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