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2000 AIME Problems
9
Classic Complex Numbers
Classic Complex Numbers
Source:
December 9, 2005
trigonometry
AMC
AIME
Problem Statement
Given that
z
z
z
is a complex number such that
z
+
1
z
=
2
cos
3
∘
,
z+\frac 1z=2\cos 3^\circ,
z
+
z
1
=
2
cos
3
∘
,
find the least integer that is greater than
z
2000
+
1
z
2000
.
z^{2000}+\frac 1{z^{2000}}.
z
2000
+
z
2000
1
.
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