2011 AIME II Problems/Problem 8: Difference between revisions
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Problem: | Problem: | ||
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>) | 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 17:06, 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:
