Complex Numbers problem

mardi 29 avril 2014

If a is a complex number, and a^2-a+1=0, then a^2011=?



I tried using De Moivre's theorem, Taking a=cosθ+isinθ, but didn't get anywhere, got stuck at

cos2θ+isin2θ-cosθ-isinθ+1=0. What do I do?





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