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
.
2000 AIME II (Problems • Answer Key • Resources) | ||
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