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2019 BMT Spring
9
Mathlete's log: this is an awfully complex problem! (BMT 2019 Discrete #9)
Mathlete's log: this is an awfully complex problem! (BMT 2019 Discrete #9)
Source:
May 26, 2019
Problem Statement
Let
z
=
1
2
(
2
+
i
2
)
z = \frac{1}{2}(\sqrt{2} + i\sqrt{2})
z
=
2
1
(
2
+
i
2
)
. The sum
∑
k
=
0
13
1
1
−
z
e
k
⋅
i
π
7
\sum_{k = 0}^{13} \dfrac{1}{1 - ze^{k \cdot \frac{i\pi}{7}}}
k
=
0
∑
13
1
−
z
e
k
⋅
7
iπ
1
can be written in the form
a
−
b
i
a - bi
a
−
bi
. Find
a
+
b
a + b
a
+
b
.
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