InterviewSolution
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InterviewSolution
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Given `alpha,beta,`respectively, the fifth and the fourth non-real roots of units, thenfind the value of`(1+alpha)(1+beta)(1+alpha^2)(1+beta^2)(1+alpha^4)(1+beta^4)` |
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Answer» As ` alpha` is the fifth nonreal root of unity, we have `alpha^(4) + alpha^(3) + alpha^(2) + alpha + 1=0` `beta ` is the fouth nonreal root of unity . Therefore, `beta^(3) + beta^(2) + beta + 1=0` Now, `( 1 + alpha )(1 + alpha^(2))(1 + alpha^(4))(1+ beta)(1+ beta^(2))(1 + beta^(3))` `= (1+ alpha + alpha^(2)+ alpha^(3) ) (1+alpha^(4)) (1+ beta + beta^(2) + beta^(3))(1+ beta^(3)) (because 1+ beta + beta^(2) + beta^(3) = 0)` `= 0` |
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