Re: exponentials to sines and cosines
- To: mathgroup at smc.vnet.net
- Subject: [mg42643] Re: exponentials to sines and cosines
- From: bobhanlon at aol.com (Bob Hanlon)
- Date: Sat, 19 Jul 2003 03:19:28 -0400 (EDT)
- References: <bf8ern$5la$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
ComplexExpand[(-1)^(1/3)]
1/2 + (I*Sqrt[3])/2
ComplexExpand[x /.Solve[x^3\[Equal]-1,x]]
{-1, 1/2 + (I*Sqrt[3])/2, 1/2 - (I*Sqrt[3])/2}
f[x_] := Evaluate[Simplify[ComplexExpand[
(1+E^(x+(-1)^(1/3)*x)+
E^((-1)^(1/3)*x+(-1)^(2/3)*x))/
E^((-1)^(1/3)*x)]]];
f[x]
(2*Cos[(Sqrt[3]*x)/2])/E^(x/2) + E^x
Bob Hanlon
In article <bf8ern$5la$1 at smc.vnet.net>, "Will Self" <wself at msubillings.edu>
wrote:
<< 1. How do I get Mathematica to rewrite (-1)^(1/3) in standard rectangular
form?
2. The following function was returned by Mathematica as the solution of a
differential equation. This function is real. How do I get Mathematica to
write it in terms of Sines and Cosines?
f[x_]=(1 + E^(x + (-1)^(1/3)*x) + E^((-1)^(1/3)*x + (-1)^(2/3)*x))/
E^((-1)^(1/3)*x)