Difference between revisions of "1997 AIME Problems/Problem 14"
Ninja glace (talk | contribs) (→Problem) |
Ninja glace (talk | contribs) (→Solution) |
||
Line 3: | Line 3: | ||
== Solution == | == Solution == | ||
+ | The solution requires use of Euler's formula: | ||
+ | <math>\displaystyle e^{i\theta}=\cos(\theta)+i\sin(\theta)</math> | ||
== See also == | == See also == | ||
* [[1997 AIME Problems]] | * [[1997 AIME Problems]] |
Revision as of 20:03, 7 March 2007
Problem
Let and
be distinct, randomly chosen roots of the equation
. Let
be the probability that
, where
and
are relatively prime positive integers. Find
.
Solution
The solution requires use of Euler's formula: