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De Moivre’s theorem states that for real numbers n and x,
exp(inx)  i sin nx  cos nx .
In particular, we get the following result:
(isin x  cos x)n  isin nx  cos nx ,
and the relationships:
sin x 
eix  eix
eix  eix
and cos x 
.
2i
2
See also: @@i@@, @@imaginary number@@, @@complex number@@.
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