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Re: minimize with complex numbers

On 8/11/08 at 6:08 AM, shammashahbaz at (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=

>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

>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.

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