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Multiple choice

If $\alpha, \beta$ are the roots of the equation $x^2 + 2x +2 =0$, then $\alpha^n + \beta^n$ is equal to

  1. $2^{\dfrac{n}{2}} cos \dfrac{n \pi}{4}$
  2. $2^{\dfrac{n}{2}+1} cos \dfrac{n \pi}{4}$
  3. $2^{\dfrac{n}{2}-1} cos \dfrac{n \pi}{4}$
  4. none of these

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