Re: Question for using complex variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg13795] Re: Question for using complex variables*From*: Tobias Oed <tobias at physics.odu.edu>*Date*: Fri, 28 Aug 1998 04:18:19 -0400*Organization*: Old Dominion University*References*: <6r10kv$fjg@smc.vnet.net> <6rravl$1bk@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Paul Abbott wrote: > > Chongdae Park wrote: > > > Here, x, y, w, and z are all real values. Then I expected > > > > Complex[x,y]*Complex[w,z]=(xw-yz)+I(xz+yw) > > First, note that > > In[1]:= ?Complex > "Complex is the head used for complex numbers." > > so, to work with complex variables in explicit form, you should not use > Complex but instead enter them directly as x+I y, etc. > > Second, ComplexExpand is the operator you want for simplifying complex > expressions (assuming that the variables x,y,w,z are real): > > In[2]:= ComplexExpand[(x + I y) (w + I z)] > Out[2]= w x - y z + I (w y + x z) Is this really what you get ? On my machine I have the result: In[1]:= ComplexExpand[(x + I y) (w + I z)] Out[1]=w x + I w y + I x z - y z To get your answer, I need to do: In[1]:= test=(x + I y) (w + I z) Out[1]= (x + I y) (w + I z) In[2]:= (Factor[Select[#,!FreeQ[#,Complex,2]&]]+Select[#,FreeQ[#,Complex,2]&])&[Expand[test]] Out[2]= w x - y z + I (w y + x z) I think the purpose of the ComplexExpand function is not to expand a product of cmplex number, but instead to help simplify expressions involving functions dealing with complex numbers: In[3]:= ??ComplexExpand ComplexExpand[expr] expands expr assuming that all variables are real. ComplexExpand[expr, {x1, x2, ... }] expands expr assuming that variables matching any of the xi are complex. Attributes[ComplexExpand] = {Protected, ReadProtected} Options[ComplexExpand] = TargetFunctions -> {Re, Im, Abs, Arg, Conjugate, Sign} For expample, if z is complex but x is real In[4]:= Re[x z] Out[4]= Re[x z] In[5]:= ComplexExpand[%,{z}] Out[5]= x Re[z] Tobias > > Cheers, > Paul > > ____________________________________________________________________ > Paul Abbott Phone: +61-8-9380-2734 > Department of Physics Fax: +61-8-9380-1014 > The University of Western Australia Nedlands WA 6907 > mailto:paul at physics.uwa.edu.au AUSTRALIA > http://www.physics.uwa.edu.au/~paul > > God IS a weakly left-handed dice player > ____________________________________________________________________