# Difference between revisions of "2011 AIME II Problems/Problem 8"

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Problem: | Problem: | ||

− | Let <math> | + | Let <math>z_1</math>, <math>z_2</math>, <math>z_3</math>, <math>\dots</math>, <math>z_{12}</math> be the 12 zeroes of the polynomial <math>z^{12} - 2^{36}</math>. For each <math>j</math>, let <math>w_j</math> be one of <math>z_j</math> or <math>iz_j</math>. Then the maximum possible value of the real part of <math>\sum_{j = 1}^{12} w_j</math> can be written as <math>m + \sqrt{n}</math>, where <math>m</math> and <math>n</math> are positive integers. Find <math>m + n</math>. |

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Solution: | Solution: |

## Revision as of 18:15, 31 March 2011

Problem:

Let , , , , be the 12 zeroes of the polynomial . For each , let be one of or . Then the maximum possible value of the real part of can be written as , where and are positive integers. Find .

Solution: