Re: Absolute value

*To*: mathgroup at smc.vnet.net*Subject*: [mg110627] Re: Absolute value*From*: Marco Masi <marco.masi at ymail.com>*Date*: Tue, 29 Jun 2010 06:59:17 -0400 (EDT)

Thanks, this gave some insight. And yet I'm struggling to get it in another form. I have to work with an expression like: FullSimplify[ Collect[ComplexExpand[ Abs[A1 E^(I \[Phi]1) ((1 + Cos[Sqrt[2] c z])/2) + AD E^(I \[Phi]D) I/Sqrt[2] Sin[Sqrt[2] c z] + A2 E^(I \[Phi]2) ((Cos[Sqrt[2] c z] - 1)/2)]^2, TargetFunctions -> {Re, Im}], A1 | A2 | AD], TrigFactor] Which does not separate A1, A2 and AD. I would like to have an output in a form like: A1^2*f1[Cos[Sqrt[2] c z],Sin[Sqrt[2] c z]] + A2^2*f2[Cos[Sqrt[2] c z],Sin[Sqrt[2] c z]] + AD^2*f3[Cos[Sqrt[2] c z],Sin[Sqrt[2] c z]], where f1, f2, and f3 are some functions of Cos[Sqrt[2] c z] and Sin[Sqrt[2] c z]. Is this possible? Regards, Mark. --- Lun 28/6/10, Peter Pein <petsie at dordos.net> ha scritto: Da: Peter Pein <petsie at dordos.net> Oggetto: Re: Absolute value A: Data: Luned=EC 28 giugno 2010, 09:05 Am Mon, 28 Jun 2010 06:30:57 +0000 (UTC) schrieb Marco Masi <marco.masi at ymail.com>: > Yes, thank you, that brough me a step forward (and yes, I forgot to > square the Abs value in the previous example... sorry for that). > > However, there is still a step which I can't accomplish. Please try > the following: FullSimplify[ ComplexExpand[ Abs[1/2 (A1 E^(I \[Phi]1) > - A2 E^(I \[Phi]2) + A1 E^(I \[Phi]1) Cos[Sqrt[2] c z] + A2 E^(I > \[Phi]2) Cos[Sqrt[2] c z])]]^2] > > I would like to have Mathematica avoiding one of the resulting Cos[2 > Sqrt[2] c z] expression, and maintain both as Cos[Sqrt[2] c z], and > then simplify. How should I proceed? > > Regards, Mark. > Hi Mark, try squaring the absolute value before using ComplexExpand: FullSimplify[ComplexExpand[ Abs[(1/2)*(A1*E^(I*\[Phi]1) - A2*E^(I*\[Phi]2) + A1*E^(I*\[Phi]1)*Cos[Sqrt[2]*c*z] + A2*E^(I*\[Phi]2)*Cos[Sqrt[2]*c*z])]^2]] --> (1/4)*Abs[A2*E^(I*\[Phi]2)*(-1 + Cos[Sqrt[2]*c*z]) + A1*E^(I*\[Phi]1)*(1 + Cos[Sqrt[2]*c*z])]^2 but I would prefer: Collect[ ComplexExpand[ Abs[(1/2)*(A1*E^(I*\[Phi]1) - A2*E^(I*\[Phi]2) + A1*E^(I*\[Phi]1)*Cos[Sqrt[2]*c*z] + A2*E^(I*\[Phi]2)*Cos[Sqrt[2]*c*z])]^2, TargetFunctions -> {Re,Im}], A1 | A2, TrigFactor] which returns A1^2*Cos[(c*z)/Sqrt[2]]^4 + A2^2*Sin[(c*z)/Sqrt[2]]^4 - (1/2)*A1*A2*Cos[\[Phi]1 - \[Phi]2]*Sin[Sqrt[2]*c*z]^2 Peter