RE: exponentials to sines and cosines
- To: mathgroup at smc.vnet.net
- Subject: [mg42660] RE: [mg42603] exponentials to sines and cosines
- From: "David Park" <djmp at earthlink.net>
- Date: Sat, 19 Jul 2003 03:19:45 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Hi Will,
Is this what you mean by standard rectangular form?
(-1)^(1/3);
step1 = % // ComplexExpand
1/2 + (I*Sqrt[3])/2
We could calculate the angle and express it in exponenetial form.
ArcTan[Re[step1], Im[step1]]
E^(I %)
% // ComplexExpand
Pi/3
E^((I*Pi)/3)
1/2 + (I*Sqrt[3])/2
For the second case, would you allow Cosh and Sinh functions? They provide
the simple real form of the expression.
(1 + E^(x + (-1)^(1/3)*x) + E^((-1)^(1/3)*x + (-1)^(2/3)*x))/
E^((-1)^(1/3)*x);
% // ComplexExpand;
% // ExpToTrig // Simplify
(Cosh[x/4] + Sinh[x/4])*((1 + 2*Cos[(Sqrt[3]*x)/2])*
Cosh[(3*x)/4] + (1 - 2*Cos[(Sqrt[3]*x)/2])*
Sinh[(3*x)/4])
David Park
djmp at earthlink.net
http://home.earthlink.net/~djmp/
From: Will Self [mailto:wself at msubillings.edu]
To: mathgroup at smc.vnet.net
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)
Thanks.