2011 AIME II Problems/Problem 8

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 iz_{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.

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Solution: