0

Unknows are two, which are complex number X and complex number Y.

Constants are sixteen, which are complex numbers A_1, A_2, B_1, B_2, C_1, C_2, D_1, D_2, E_1, E_2, F_1, F_2, G_1, G_2, H_1 and H_2.

Equation (1): XA_1+ YB_1+ XYC_1+ conj(X)D_1 + Yconj(X)E_1 + Xconj(X)F_1 + XYconj(X)G_1+ H_1= 0 

Equation (2): XA_2+ YB_2+ XYC_2+ conj(Y)D_2 + Xconj(Y)E_2 + Yconj(Y)F_2 + XYconj(Y)G_2+ H_2= 0

where,

conj(X)= complex conjugate of X and conj(Y)= complex conjugate of Y.

|X|<=1 and |Y|<=1

How to solve for the two unknowns when the equations contain the complex conjugate?

m4n0
  • 29,823
  • 27
  • 76
  • 89
Hansel Dsilva
  • 1
  • 2
  • 1
    I’m voting to close this question because it belongs to https://math.stackexchange.com/ – m4n0 Oct 14 '21 at 01:25
  • let: X=(r+ij) and Y=(R+Ij); XA_1+ YB_1+ XYC_1+ conj(X)D_1 + Yconj(X)E_1 + Xconj(X)F_1 + XYconj(X)G_1+ H_1= 0 ==> (r+ij)A_1+ (R+Ij)B_1+ (r+ij)(R+Ij)C_1+ conj((r+ij))D_1 + (R+Ij)conj((r+ij))E_1 + (r+ij)conj((r+ij))F_1 + (r+ij)(R+Ij)conj((r+ij))G_1+ H_1= 0 ==> (r+ij)A_1+ (R+Ij)B_1+ (r+ij)(R+Ij)C_1+ (r-ij)D_1 + (R+Ij)(r-ij)E_1 + (r+ij)(r-ij)F_1 + (r+ij)(R+Ij)(r-ij))G_1+ H_1= 0 ==> ... ==> ()+()j= 0 (NOTE THAT j=sqrt(-1); python code might be best, has it complex number support) – Andrew Mar 03 '22 at 15:27

0 Answers0