Re: minimize with complex numbers

*To*: mathgroup at smc.vnet.net*Subject*: [mg91258] Re: minimize with complex numbers*From*: Bill Rowe <readnews at sbcglobal.net>*Date*: Tue, 12 Aug 2008 04:45:52 -0400 (EDT)

On 8/11/08 at 6:08 AM, shammashahbaz at yahoo.com (shama shahbaz) wrote: >hi , when i use minimize command with real numbers i get the >required answer but with complex number it doesnt give me any answer or er= ror >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 You have syntax issues here. In Mathematica, x[2] is the function x to be evaluated at 2. I doubt this is what you had in mind. Also, the symbol i is not defined. You want the built-in symbol I which is the square root of minus 1. However, fixing the syntax issues will not get you what you want. Minimize only works with real valued expressions. If I fix your syntax problems by substituting x for x[1], y for x[2] and I for i then Expand, I get In[5]:= ((1 + I)*x + (1 - I)*y)^2 + (x + y)^2 // Expand Out[5]= (1 + 2 I) x^2 + 6 y x + (1 - 2 I) y^2 which is clearly only real valued for the case where x^2 == y^2. Minimize is restricted to real valued functions since for complex variables x, y x > y is not defined.