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Let alpha and beta be two roots of the e...

Let `alpha` and `beta` be two roots of the equation `x^(2) + 2x + 2 = 0`. Then `alpha^(15) + beta^(15)` is equal to

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The correct Answer is:
4
Roots are `(-1+-i)impliesalpha^(15)+beta^(15)=-[(1+i)^(15)+(1-i)^(15)]=-2^(15//2)[2cos(15pi//4)]`
`=-2^(15//2)xxsqrt(2)=-256`
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