Let P(z)=z^{8}+(4 \sqrt{3}+6) z^{4}-(4 \sqrt{3}+7). What is the minimum perimeter among all the 8-sided polygons in the complex plane whose vertices are precisely the zeros of P(z) ?
Answer Choices
A. 4 \sqrt{3}+4
B. 8 \sqrt{2}
C. 3 \sqrt{2}+3 \sqrt{6}
D. 4 \sqrt{2}+4 \sqrt{3}
E. 4 \sqrt{3}+6