Difference between revisions of "2000 AIME II Problems/Problem 9"
(→Solution) |
(→Solution) |
||
| Line 3: | Line 3: | ||
== Solution == | == Solution == | ||
| − | Note that if z is on the unit circle in the complex plane, then | + | Note that if z is on the unit circle in the complex plane, then <math>z = e^{i\theta} = cos \theta + isin \theta</math> and <math>\frac 1z= e^{-i\theta} = cos \theta - isin \theta</math> |
| − | + | ||
| + | Let <math>z = a + bi</math> | ||
== See also == | == See also == | ||
{{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 18:40, 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 
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 | ||
