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From: Arnold on 23 Jan 2010 07:35
How by means of Mathematica to transform (Cos [x] +I* Sin [x]) ^n in Cos [n*x] +I*Sin [n*x]?

Thanks.

From: Adriano Pascoletti on 24 Jan 2010 05:37
FullSimplify[(Cos[x] + I*Sin[x])^n, Element[n, Integers]] // ComplexExpand


Adriano Pascoletti

2010/1/23 Arnold <sender999ster(a)gmail.com>

> How by means of Mathematica to transform (Cos [x] +I* Sin [x]) ^n in Cos
> [n*x] +I*Sin [n*x]?
>
> Thanks.
>
>
From: Sjoerd C. de Vries on 24 Jan 2010 05:37
Hi Arnold,

ExpToTrig[PowerExpand[FullSimplify[(Cos[x] + I*Sin[x])^n]]]

but this is actually only true for n integer OR x positive reals.

Cheers -- Sjoed

On Jan 23, 2:35 pm, Arnold <sender999s...(a)gmail.com> wrote:
> How by means of Mathematica to transform (Cos [x] +I* Sin [x]) ^n in Cos[n*x] +I*Sin [n*x]?
>
> Thanks.


From: Patrick Scheibe on 24 Jan 2010 05:36
Hi,

what about

ExpToTrig@
Simplify[TrigToExp[(Cos[x] + I*Sin[x])^n], n \[Element] Integers]

?

Cheers
Patrick

On Sat, 2010-01-23 at 07:36 -0500, Arnold wrote:
> How by means of Mathematica to transform (Cos [x] +I* Sin [x]) ^n in Cos [n*x] +I*Sin [n*x]?
>
> Thanks.
>


From: DC on 24 Jan 2010 05:39
In[4]:= FullSimplify[Cos[x] + I Sin[x]]

Out[4]= E^(I x)

In[7]:= FullSimplify[(Cos[x] + I Sin[x])^n,
Assumptions -> {n \[Element] Integers}]

Out[7]= E^(I n x)

-Francesco

On 01/23/2010 12:35 PM, Arnold wrote:
> How by means of Mathematica to transform (Cos [x] +I* Sin [x]) ^n in Cos [n*x] +I*Sin [n*x]?
>
> Thanks.
>

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