MathDB

Complex roots of a polynomial [2011.II.8]

Source:

March 31, 2011

algebrapolynomialanalytic geometrygeometrygeometric transformationreflectiontrigonometry

Problem Statement

Let

z_1,z_2,z_3,\dots,z_{12}

be the 12 zeroes of the polynomial

z^{12}-2^{36}

. For each

j

, let

w_j

be one of

z_j

i z_j

. Then the maximum possible value of the real part of

\displaystyle\sum_{j=1}^{12} w_j

can be written as

m+\sqrt{n}

where

m

and

n

are positive integers. Find

m+n