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

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Problem: | Problem: | ||

− | Let <math>z_{1}, z_{2}, ... , z_{12}</math> be the 12 zeros of the polynomial z^12-2^36. For each j, let <math>w_{j }</math>be one of <math>z_{j}</math> or | + | Let <math>z_{1}, z_{2}, ... , z_{12}</math> be the 12 zeros of the polynomial <math>z^12-2^36</math>. For each j, let <math>w_{j }</math>be one of <math>z_{j}</math> or ''i''<math>z_{j}</math>. Then the maximum possible value of the real part of (somebody who knows how please create in an equation) SUM j=1 to 12 (<math>w_{j}</math>) |

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 18:05, 31 March 2011

Problem:

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

Solution: