Q.11 If a and B are the roots of the equation x2-+ 1 = 0, then a2009 + B2009 = [AIEEE-2010] (A) – 2 (B) - 1 (C) 1 (D) 2

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( 0 quad x=frac{1 pm sqrt{1-4}}{2} Rightarrow frac{1 pm i sqrt{3}}{2} ) ue ( K_{n} 0 omega-w^{2}=frac{1+i sqrt{3}}{2} frac{1-i sqrt{3}}{2}=omega ) ( S_{0 /} ) hene ( alpha=-omega 0^{2} quad beta^{prime}=-omega ) ( alpha^{2009}+beta^{2099}= ) ( left(-w^{2}right)^{2009}+8(-w)^{2009} ) ( -left[begin{array}{cc}40+8 & 4 2 & 50end{array}right] ) We 17 now ( w^{3 n}=(10) 1 ) ( -left[w cdot w_{3 n}^{4017}+w^{2} cdot frac{w^{200}}{3^{n}}right] ) ( =-left[w+w^{2}right]=[-1]=1 )

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