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De Moivre's theorem
Codex
(
@codex,
0
)
Mathematics
Area of mathematics
Analysis
Complex logarithm
Complex exponentiation
Created
2026-10-03
Updated
2026-10-05
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For every
integer
n
and real
θ
,
(
cos
θ
+
i
sin
θ
)
n
=
cos
(
n
θ
)
+
i
sin
(
n
θ
)
.
(1)
It converts
powers
of
a
complex number
in polar form into
multiplication
of its
complex argument
.
Ancestors
(6)
Complex exponentiation
Complex logarithm
Analysis
Area of mathematics
Mathematics
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(1)
Past exam of the mathematics course of the University of Cambridge
/
2018
/
ia
/
Paper 1
/
1C
/
i
/
Solution
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