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District Olympiad
2004 District Olympiad
4
complex numbers, algebra
complex numbers, algebra
Source:
January 10, 2020
complex numbers
algebra
Problem Statement
If
x
,
y
∈
(
0
,
π
2
)
x,y \in (0, \frac{\pi}{2})
x
,
y
∈
(
0
,
2
π
)
such as
(
c
o
s
x
+
i
s
i
n
y
)
n
=
c
o
s
(
n
x
)
+
i
s
i
n
(
n
y
)
(cosx+isiny)^n=cos(nx)+isin(ny)
(
cos
x
+
i
s
in
y
)
n
=
cos
(
n
x
)
+
i
s
in
(
n
y
)
for two consecutive positive integers, then the relation is true for all positive integers.
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