My Math Forum linear equation with complex variables

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 November 15th, 2018, 02:53 PM #1 Newbie   Joined: Nov 2016 From: Aus Posts: 24 Thanks: 0 G'day all, How to solve the following equation please, (A, B, C,.. real constants, while X, Y are complex variables: knowing that the equations are determinate (applied for several inputs of data so that the number of variables=number of equations A+iB= Real [(C.Real(x)+D.Real(y)+ E.imaginary(X)+F.imaginary(Y))]+ Imaginary[ (G.Real(x)+H.Real(y)+ I.imaginary(X)+J.imaginary(Y))] ----Eq(1) AA+iBB= Real (K.Real(x)+L.Real(y)+ M.imaginary(X)+N.imaginary(Y))+ Imaginary[(Q.Real(x)+R.Real(y)+ S.imaginary(X)+T.imaginary(Y))]-----Eq(2) Two possibilities : sol-1 the real part for RS = the Real part in the LS the imaginary part for RS = the Real part in the LS noting that each real part has both real&imaginary variables A=[(C.Real(x)+D.Real(y)+ E.imaginary(X)+F.imaginary(Y))]----1 B=[(G.Real(x)+H.Real(y)+ I.imaginary(X)+J.imaginary(Y))]--2 AA= [/B](K.Real(x)+L.Real(y)+ M.imaginary(X)+N.imaginary(Y))--3 BB=[(Q.Real(x)+R.Real(y)+ S.imaginary(X)+T.imaginary(Y))]--4 OR The real parts equal the real variables, the imaginary part LS= the imaginary variables , as follows A=[(C.Real(x)+D.Real(y)+[ (G.Real(x)+H.Real(y)] B=[E.imaginary(X)+F.imaginary(Y))]+[ (I.imaginary(X)+J.imaginary(Y))] AA =(K.Real(x)+L.Real(y)+ [(Q.Real(x)+R.Real(y)] BB=[M.imaginary(X)+N.imaginary(Y))+ Imaginary[S.imaginary(X)+T.imaginary(Y))] Thanks Last edited by skipjack; November 16th, 2018 at 10:33 AM.
 November 18th, 2018, 04:46 PM #2 Newbie   Joined: Nov 2016 From: Aus Posts: 24 Thanks: 0 To correct there is only one equation as follows: (I) is imaginary unit A+I*B= [(C.Real(x)+D.Real(y)+ E.imaginary(X)+F.imaginary(Y))]+ I*[ (G.Real(x)+H.Real(y)+ M.imaginary(X)+J.imaginary(Y))] ---- This equation should satisfy several boundary conditions. at each point of these boundary the constant [C,D,E,F,G,H,M,J] are known. No of points is (N) X, Y are vectors of variables of (M) terms (X1,X2,X3,....XM) N=2M
 November 18th, 2018, 05:07 PM #3 Senior Member   Joined: Sep 2016 From: USA Posts: 635 Thanks: 401 Math Focus: Dynamical systems, analytic function theory, numerics This is almost completely unintelligible. I suggest asking the question again and using standard notation and ideally, latex. Thanks from Denis and idontknow
 November 22nd, 2018, 02:52 AM #4 Newbie   Joined: Nov 2016 From: Aus Posts: 24 Thanks: 0 See attached, please System of linear equations

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