1984 AIME Problems/Problem 8
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 .
Also,
From above, you notice that . Therefore, the solutions are all of the ninth roots of unity that are not the third roots of unity. After checking, the only angle is .
See also
1984 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 7 |
Followed by Problem 9 | |
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