Re: Absolute value

*To*: mathgroup at smc.vnet.net*Subject*: [mg110605] Re: Absolute value*From*: "David Park" <djmpark at comcast.net>*Date*: Mon, 28 Jun 2010 02:27:34 -0400 (EDT)

Maybe someone will give a more direct calculation, but otherwise this is slightly on the tricky side. Paste the following into a notebook and evaluate. Print["Initial complex expression:"] step1 = Exp[I phi1] + Exp[I*phi2] Print["Convert to trigonometric form."] step2 = step1 // ExpToTrig Print["Calculate the Abs value squared and expand to real + imaginary \ form, with the imaginary part zero."] step3 = ComplexExpand[Abs[step2]^2, TargetFunctions -> {Re, Im}] Print["Use TrigFactor."] step4 = step3 // TrigFactor Print["Take the square root and simplify"] Simplify[Sqrt[step4], {phi1, phi2} \[Element] Reals] 1) It seemed easier to calculate Abs^2 and then take the square root at the end. 2) We need to use ComplexExpand to expand a complex expression to the form (real part) + I (imaginary part) and since the imaginary part is already zero we have to use the TargetFunctions option to get this to evaluate to the extent that we want. 3) We have to use TrigFactor to obtain the trigonometric form you are looking for. How did I know that? I didn't really. I tried TrigExpand, TrigReduce and then TrigFactor. But since the expression looks like one that could be factored I should have tried TrigFactor first. 4) Finally we take the square root and simplify using real variable assumptions. Both the Complex and ComplexExpand Function pages need more explicit notes and examples to point users in the right direction. David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: Marco Masi [mailto:marco.masi at ymail.com] I would like to calculate the absolute value of complex quantities. For example Abs[Exp[I phi1]+Exp[I*phi2]], which sould give 2 (1+cos(phi1-phi2)). However it does not work. I tried to use real numbers as assumtion, but it always answers "Abs[Exp[I phi1]+Exp[I*phi2]]". What am I doing wrong? Regards, Mark.