AMC 12A 2009 Problem 21

Let p(x)=x^{3}+a x^{2}+b x+c, where a, b, and c are complex numbers. Suppose that

p(2009+9002 \pi i)=p(2009)=p(9002)=0 \text {. }

What is the number of nonreal zeros of x^{12}+a x^{8}+b x^{4}+c ?

Answer Choices
A. 4
B. 6
C. 8
D. 10
E. 12