Difference between revisions of "1984 AIME Problems/Problem 8"
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[[Category:Intermediate Trigonometry Problems]] | [[Category:Intermediate Trigonometry Problems]] |
Revision as of 22:11, 30 November 2007
Problem
The equation has complex roots with argument
between
and
in the complex plane. Determine the degree measure of
.
Solution
If is a root of
, then
. The polynomial
has all of its roots with absolute value
and argument of the form
for integer
.
This reduces to either
or
. But
can't be
because if
, then
and
, a contradiction. This leaves
.
See also
1984 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |