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(i) If alpha,beta be the imaginary cube ...

(i) If `alpha`,`beta` be the imaginary cube root of unity, then show that `alpha^4+beta^4+alpha^-1beta^-1=0`

Text Solution

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`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`
...
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