Re: Simplifying Complex expression
- To: mathgroup at smc.vnet.net
- Subject: [mg43091] Re: Simplifying Complex expression
- From: Paul Abbott <paul at physics.uwa.edu.au>
- Date: Tue, 12 Aug 2003 04:43:05 -0400 (EDT)
- Organization: The University of Western Australia
- References: <bgv903$5i3$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
In article <bgv903$5i3$1 at smc.vnet.net>,
Helge Andersson <helge at envic.chalmers.se> wrote:
> I'm interested in one of the solution to the the following equation:
> y=3 x^2-2 x^3
> in the x-intervall 0 to 1 and for y-values between 0 and 1
> With Solve I got three solutions where two of them are complex in general.
> However, it is possible to plot each of them Using the Plot-command in the
> desired domain which I interpretate as they are real-valued with my
> specific conditions. My problem is to simplify the general complex solution
> to one that is real in the domain 0 to 1. The solution that I specifically
> is interested in is the following given in InputForm:
>
> 1/2 - (1 - I*Sqrt[3])/(4*(1 + 2*Sqrt[-1 + y]*Sqrt[y] - 2*y)^(1/3)) -
> ((1 + I*Sqrt[3])*(1 + 2*Sqrt[-1 + y]*Sqrt[y] - 2*y)^(1/3))/4
>
> Could someone give me an idea to perform this (for example with Simplify
> Command)
After computing the solutions,
solns = x /. Solve[y == 3 x^2 - 2 x^3, x]
one can use ComplexExpand to obtain explicitly real forms,
Simplify[ComplexExpand[Re[solns],TargetFunctions -> {Re, Im}], 0<y< 1]
One needs to verify that the imaginary part is identically zero.
Simplify[ComplexExpand[Im[solns],TargetFunctions -> {Re, Im}], 0<y< 1]
Cheers,
Paul
--
Paul Abbott Phone: +61 8 9380 2734
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