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minimize with complex numbers

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 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

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