2011 AIME II Problems/Problem 8

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Problem:

Let $z_{1}, z_{2}, ... , z_{12}$ be the 12 zeros of the polynomial $z^12-2^36$. For each j, let $w_{j }$be one of $z_{j}$ or i$z_{j}$. Then the maximum possible value of the real part of (somebody who knows how please create in an equation) SUM j=1 to 12 ($w_{j}$) can be written as m+root(n), where m and n are positive integers. Find m+n.


Solution:

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