Difference between revisions of "2000 AIME II Problems/Problem 9"
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Finally, the least integer greater than <math>-1</math> is <math>\boxed{000}</math>. | Finally, the least integer greater than <math>-1</math> is <math>\boxed{000}</math>. | ||
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{{AIME box|year=2000|n=II|num-b=8|num-a=10}} | {{AIME box|year=2000|n=II|num-b=8|num-a=10}} |
Revision as of 19:34, 18 March 2008
Problem
Given that is a complex number such that , find the least integer that is greater than .
Solution
Note that if z is on the unit circle in the complex plane, then and
We have and Alternatively, we could let and solve to get
Using De Moivre's Theorem we have , , so
We want
Finally, the least integer greater than is .
2000 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |