1997 AIME Problems/Problem 14
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 the use of Euler's formula:
If 
, where k is any constant, the equation reduces to:
\begin{eqnarray*}
e^{2\pi ik}&=&\cos(2\pi k)+i\sin(2\pi k)
&=&1+0i
&=&1+0
&=&1
\end{eqnarray*}
