Re: minimize with complex numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg91255] Re: minimize with complex numbers*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Tue, 12 Aug 2008 04:45:19 -0400 (EDT)*Organization*: The Open University, Milton Keynes, UK*References*: <g7p32p$b07$1@smc.vnet.net>

shama shahbaz wrote: > when i use minimize command with real numbers i get the required answer but > with complex number it doesnt give me any answer or error > > Syntax::sntxb : Expression cannot begin with "(1+1 i) ` x[1]+(1-1 i) ` x[2]". > Syntax::tsntxi : "(1+1 i) ` x[1]" is incomplete; more input is needed. > Syntax::sntxi : Incomplete expression; more input is needed. > > > My minimize expression is > > ((1+1i)*x[1] +(1-1i)*x[2] )^2 +(x[1]+x[2])^2 > > in methamatica it becomes > > Minimize[{( x[1]+x[2])2 > +((1+1i)x[1]+(1-1 i)x[2])2},{x[1],x[2]}] > > > i want my answer to be in complex number come somebody tell me where i am wrong Minimize requires that all functions present in the input be real-valued. (It does not work with complex coefficient either.) Note that the code you posted does not contain the imaginary unit, which is denoted in Mathematica by I (capital i). You must have some other error(s) since, having used the correct symbol for the imaginary unit, I did not get the same message as yours. In[1]:= expr = ((1 + 1 i)*x[1] + (1 - 1 i)*x[2])^2 + (x[1] + x[2])^2 Minimize[expr, {x[1], x[2]}] Out[1]= (x[1] + x[2])^2 + ((1 + i) x[1] + (1 - i) x[2])^2 Out[2]= {0, {x[1] -> Piecewise[{{-1, i == 0}}], x[2] -> Piecewise[{{0, i > 0 || i < 0}}, 1]}} In[3]:= expr = ((1 + 1 I)*x[1] + (1 - 1 I)*x[2])^2 + (x[1] + x[2])^2 Minimize[expr, {x[1], x[2]}] Out[3]= (x[1] + x[2])^2 + ((1 + I) x[1] + (1 - I) x[2])^2 During evaluation of In[3]:= Minimize::objc: The objective function \ (x[1]+x[2])^2+((1+I) x[1]+(1-I) x[2])^2 contains a nonreal constant \ 1+I. >> Out[4]= Minimize[(x[1] + x[2])^2 + ((1 + I) x[1] + (1 - I) x[2])^2, {x[1], x[2]}] Regards, -- Jean-Marc