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 School of Physics, M013 Fax: +61 8 9380 1014 The University of Western Australia (CRICOS Provider No 00126G) 35 Stirling Highway Crawley WA 6009 mailto:paul at physics.uwa.edu.au AUSTRALIA http://physics.uwa.edu.au/~paul