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I Isolating a complex-valued variable

  1. Aug 15, 2016 #1
    If ## A, B, ## and ## C## are complex-valued variables, is there an easy way to algebraically solve for ##A## without splitting the variables into their real and imaginary parts? For example:

    $$ AB^* = 20AB - A^*C + B^*C^* $$

    can be isolated for ##A## but only if the real and imaginary parts are distinguished. That's fine. I am just wondering if there are any other methods to solve for ## A ## in the above equation as only a function of ##B, B^*, C, C^* ## (i.e. not ##A^*##)
  2. jcsd
  3. Aug 20, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
  4. Aug 20, 2016 #3


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    Staff: Mentor

    I don't think there is a useful approach that avoids splitting A into components.
  5. Aug 20, 2016 #4


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    Hey TheCanadian.

    Apart from getting the variable separated (which is what you would need to do to get an explicit function of a variable), you are going to have to also deal with the conjugate variable A*.

    You could divide by A* to remove that variable and then look at some new variable which is a function of A and A* [or some other transformation which is a function of both] so that your new variable U is such that U = f(A,A*) and then solve for your A and A* once you solve for U.

    I should point out though that algebraically solving with x + iy and a single complex variable will generate the same solution so if you can do it with the two dimensional version then it would be recommended.
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