1984 AIME Problems/Problem 8
Problem
The equation has complex roots with argument
between
and
in thet complex plane. Determine the degree measure of
.
Solution
If is a root of
, then
. The polynomial
has all of its roots with absolute value 1 and argument of the form
for integer
.
This reduces to either 120 or 160. But
can't be 120 because if
, then
and
, a contradiction. This leaves
.