MathDB
Problems
Contests
National and Regional Contests
China Contests
National High School Mathematics League
2000 National High School Mathematics League
6
Complex Number
Complex Number
Source: 2000 National High School Mathematics League, Exam One, Problem 6
March 10, 2020
complex numbers
Problem Statement
Let
ω
=
cos
π
5
+
i
sin
π
5
\omega=\cos\frac{\pi}{5}+\text{i}\sin\frac{\pi}{5}
ω
=
cos
5
π
+
i
sin
5
π
, which equation has roots
ω
,
ω
3
,
ω
7
,
ω
9
\omega,\omega^3,\omega^7,\omega^9
ω
,
ω
3
,
ω
7
,
ω
9
?
(A)
x
4
+
x
3
+
x
2
+
x
+
1
=
0
(B)
x
4
−
x
3
+
x
2
−
x
+
1
=
0
\text{(A)}x^4+x^3+x^2+x+1=0\qquad\text{(B)}x^4-x^3+x^2-x+1=0
(A)
x
4
+
x
3
+
x
2
+
x
+
1
=
0
(B)
x
4
−
x
3
+
x
2
−
x
+
1
=
0
(C)
x
4
−
x
3
−
x
2
+
x
+
1
=
0
(D)
x
4
+
x
3
+
x
2
−
x
+
1
=
0
\text{(C)}x^4-x^3-x^2+x+1=0\qquad\text{(D)}x^4+x^3+x^2-x+1=0
(C)
x
4
−
x
3
−
x
2
+
x
+
1
=
0
(D)
x
4
+
x
3
+
x
2
−
x
+
1
=
0
Back to Problems
View on AoPS