Let α and β be two roots of


Let $\alpha$ and $\beta$ be two roots of the equation $x^{2}+2 x+2=0$, then $\alpha^{15}+\beta^{15}$ is equal to :

  1. 512

  2. $-512$

  3. $-256$

  4. 256

Correct Option: , 3


We have




$\therefore \quad \mathrm{x}=\underset{\substack{a(k t)}}{-(1+\mathrm{i})}-\underset{\substack{\text { p(let) }}}{ }(1-\mathrm{i})$

So, $\quad \alpha^{15}+\beta^{15}=\left(\alpha^{2}\right)^{7} \alpha+\left(\beta^{2}\right)^{7} \beta$



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