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9
2013 HMMT Algebra #9: Sum of Complex Numbers
2013 HMMT Algebra #9: Sum of Complex Numbers
Source:
February 17, 2013
HMMT
AMC
AIME
Problem Statement
Let
z
z
z
be a non-real complex number with
z
23
=
1
z^{23}=1
z
23
=
1
. Compute
∑
k
=
0
22
1
1
+
z
k
+
z
2
k
.
\sum_{k=0}^{22}\dfrac{1}{1+z^k+z^{2k}}.
k
=
0
∑
22
1
+
z
k
+
z
2
k
1
.
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