Talk:De Moivre's formula
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De Moivre's formula is actually true for all complex numbers x and all real numbers n, but this requires careful extension of several functions to the complex plane. <-- Loisel I'm not so sure this makes any sense.
Thanks for pointing that out; n has to be an integer. x can be complex however, since Euler's formula
- e^(ix) = cos(x) + i sin(x)
works for all complex x. --AxelBoldt
Is the function described as a [multivalued function]? in fact a periodic function?
- Yes it is. It is 2π periodic, because sin and cos are. --AxelBoldt
Is the function described as a multivalued function in fact a function? If so, what is the domain of this function? z,w being fixed chosen numbers, it is is some sense rather a multivalued constant, isn't it? (I mean, a constant can be seen as a nullary function, but this would be even more nonsense hair-splitting... and again, I can't see on what domain it is defined - don't say the empty set, because it is well known that there is only one universal function defined on this set, and it definetely has not multiple complex values.) — MFH: Talk 19:46, 10 May 2005 (UTC)
proof
Is the proof in the article the original proof of the formula? I mean, is it the way DeMoivre obtained or proved it?
Since DM's formula is a lot easier to prove using Euler's formula, I see no other reason for this proof to be in the article (except curiosity)... -- Euyyn (March 26 2005, 2346 GMT)