Difference between revisions of "2000 AIME II Problems/Problem 9"
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== Solution == | == Solution == | ||
| − | Note that if z is on the unit circle in the complex plane, then <math>z = e^{i\theta} = cos \theta + | + | Note that if z is on the unit circle in the complex plane, then <math>z = e^{i\theta} = \cos \theta + i\sin \theta</math> and <math>\frac 1z= e^{-i\theta} = \cos \theta - i\sin \theta</math> |
| + | We have | ||
Let <math>z = a + bi</math> | Let <math>z = a + bi</math> | ||
Revision as of 17:43, 3 January 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
Let 
See also
| 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 | ||
