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If alpha is non real and alpha="^5sqrt(1...

If `alpha` is non real and `alpha="^5sqrt(1)` then value of `2^|1+alpha+alpha^2+alpha^-2-alpha^-1|` is equal to

Text Solution

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`|1+alpha+alpha^2+1/alpha^2-1/alpha|`
`|(alpha^2+alpha^3+alpha^4+1+alpha-2alpha)/alpha^2|`
`|-2alpha/alpha^2|`
`=2^|-2/alpha|`
`=2^(2/|alpha|`
`2^2`
`4`
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