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Re: The formula of Abraham Moivre

• To: mathgroup at smc.vnet.net
• Subject: [mg106849] Re: [mg106792] The formula of Abraham Moivre
• From: "David Park" <djmpark at comcast.net>
• Date: Sun, 24 Jan 2010 05:47:07 -0500 (EST)
• References: <4167406.1264250638568.JavaMail.root@n11>

Doing it in steps:

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

(1/2 (-E^(-I x) + E^(I x)) + 1/2 (E^(-I x) + E^(I x)))^n  
E^(I n x)  
Cos[n x] + I Sin[n x] 


David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark/  


From: Arnold [mailto:sender999ster at gmail.com] 

How by means of Mathematica to transform (Cos [x] +I* Sin [x]) ^n in Cos
[n*x] +I*Sin [n*x]?

Thanks.