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 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)

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