Let \(P(z) = z^8 + \left(4\sqrt{3} + 6\right)z^4 - \left(4\sqrt{3} + 7\right)\). What is the minimum perimeter among all the 8-sided polygons in the complex plane whose vertices are precisely the zeros of P(z)?
Let \(P(z) = z^8 + \left(4\sqrt{3} + 6\right)z^4 - \left(4\sqrt{3} + 7\right)\).
What is the minimum perimeter among all the 8-sided polygons in the complex plane whose vertices are precisely the zeros of P(z)?
see: https://artofproblemsolving.com/wiki/index.php/2011_AMC_12B_Problems/Problem_24