Difference between revisions of "2001 AIME II Problems/Problem 14"
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== Problem == | == Problem == | ||
| + | There are <math>2n</math> complex numbers that satisfy both <math>z^{28} - z^{8} - 1 = 0</math> and <math>\mid z \mid = 1</math>. These numbers have the form <math>z_{m} = \cos\theta_{m} + i\sin\theta_{m}</math>, where <math>0\leq\theta_{1} < \theta_{2} < \ldots < \theta_{2n} < 360</math> and angles are measured in degrees. Find the value of <math>\theta_{2} + \theta_{4} + \ldots + \theta_{2n}</math>. | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| − | + | {{AIME box|year=2001|n=II|num-b=13|num-a=15}} | |
Revision as of 00:45, 20 November 2007
Problem
There are 
complex numbers that satisfy both 
and 
. These numbers have the form 
, where 
and angles are measured in degrees. Find the value of 
.
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.
See also
| 2001 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 13 |
Followed by Problem 15 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
