Simultaneous equation with Complex Numbers

  1. Solve the following simultaneous equations for the complex variables i1 and i2.

    2= (3-j)i1 - (5-j2)i2………………(1)
    12 = (2+j)i1 + (1+j6)i2………………(2)


    Not sure how to attempt this question please can you help.

    Thanking you in advance

    Jake
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. tiny-tim

    tiny-tim 26,053
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Jake! Welcome to PF! :smile:

    Solve it the same way you would for real simultaneous equations :wink:

    (and use eg 1/(3-j) = (3+j)/(32-j2))
     
  4. t-t Please excuse my ignorance but I am learning out of a book and need a push in the right direction. Is it possible to show me step by step the correct approach as my head is spinning.
     
  5. tiny-tim

    tiny-tim 26,053
    Science Advisor
    Homework Helper

    Sorry, Jake, this forum doesn't work that way. :redface:

    Show us how you would solve this if all the coefficients were real. :smile:
     
  6. Well the approach I would use is to make either i1 or i2 equal on line 1 + 2 by multiplying by the value of the opposite lines. Lets call them now line 3 + 4. Then I would subtract 4 from 3. This would leave only 1 unknown.
     
  7. Still don't understand can anyone else help?
     
  8. It's a linear system of 2 equations with two variables. You can use the method of determinants (Cramer's rule). One determinant is:

    [tex]
    \Delta = \left|\begin{array}{cc}
    3 - j & 5 - 2 j \\

    2 + j & 1 + 6 j
    \end{array}\right| = (3 - j)(1 + 6 j) - (2 + j)(5 - 2 j) = 3 + 18 j - j - 6 j^2 - 10 + 4 j - 5 j + 2 j^2 = -3 + 16 j
    [/tex]
     
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