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November 15th, 2018, 02:53 PM   #1
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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))]

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Last edited by skipjack; November 16th, 2018 at 10:33 AM.
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November 18th, 2018, 04:46 PM   #2
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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
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November 18th, 2018, 05:07 PM   #3
SDK
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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
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November 22nd, 2018, 02:52 AM   #4
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See attached, please

System of linear equations
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