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)|)/64` 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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