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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)?

 Jan 29, 2019
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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

 

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 Jan 29, 2019

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