Let p(x) = x^3 + ax^2 + bx + c, where a,b,c are complex numbers. Suppose that p(2009 + 9002\pi i) = p(2009) = p(9002) = 0.

What is the number of non-real zeros of x^{12} + ax^8 + bx^4 + c?

Source: AMC 12A, 2009

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