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SMO 2013 Junior Round 1 Question 3

SMO · SMO 2013 Junior Round 1

Question 3

If a complex number $x$ satisfies $x^2+x+1=0$, find $x^{49}+x^{50}+x^{51}+x^{52}+x^{53}$.
  1. -1
  2. $-1/2$
  3. 0
  4. $1/2$
  5. 1