Not really complex

Algebra Level 4

Suppose xx is a complex number such that 4x2+2x+1=04x^2+2x+1=0. Then,

x3+x6+x9+x12+=ab\large x^3+x^6+x^9+x^{12}+\ldots = \frac ab

where aa and b b are coprime positive integers. Find the value of a+ba+b.

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