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

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Problem: | 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}) | + | Let <math>z_{1}, z_{}2, ... , z_{12}</math> 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. | can be written as m+root(n), where m and n are positive integers. Find m+n. | ||

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Solution: | Solution: |

## Revision as of 18:04, 31 March 2011

Problem:

Let 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: