2000 AIME II Problems/Problem 9
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 .
See also
2000 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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