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 $z=\cos 3^\circ + i\sing 3^\circ$ (Error compiling LaTeX. Unknown error_msg)
Using DeMoivre's theorem we can now find .
See also
2000 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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All AIME Problems and Solutions |