MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
BMT Problems
2021 BMT
20
BMT 2021 General p20
BMT 2021 General p20
Source:
September 27, 2023
algebra
complex numbers
Problem Statement
For some positive integer
n
n
n
,
(
1
+
i
)
+
(
1
+
i
)
2
+
(
1
+
i
)
3
+
.
.
.
+
(
1
+
i
)
n
=
(
n
2
−
1
)
(
1
−
i
)
(1 + i) + (1 + i)^2 + (1 + i)^3 + ... + (1 + i)^n = (n^2 - 1)(1 - i)
(
1
+
i
)
+
(
1
+
i
)
2
+
(
1
+
i
)
3
+
...
+
(
1
+
i
)
n
=
(
n
2
−
1
)
(
1
−
i
)
, where
i
=
−
1
i = \sqrt{-1}
i
=
−
1
. Compute the value of
n
n
n
.
Back to Problems
View on AoPS