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Math Help - conjugate of complex number

  1. #1
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    conjugate of complex number

    To find the conjugate of a complex number, we know that if it is of the form a+ib, then the conjugate is a-ib. Now say I have a very huge expression containing complex numbers in numerators and denominators which is very tough to reduce in the form a+ib. I have to find its conjugate. Then if I replace every i by -i in the expression, will this resultant expression be the required conjugate?
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  2. #2
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    I don't think this will work in all cases, can you post the equation in question?
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  3. #3
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    conjugate of a complex number

    Quote Originally Posted by pickslides View Post
    I don't think this will work in all cases, can you post the equation in question?
    I have attached the expression in pdf file.
    Attached Files Attached Files
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  4. #4
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    That method will work. If you replace \lambda and \eta by their conjugates (and if all the other symbols k, x, y represent real quantities), then you will get a valid expression for the conjugate of P.
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    Quote Originally Posted by Opalg View Post
    That method will work. If you replace \lambda and \eta by their conjugates (and if all the other symbols k, x, y represent real quantities), then you will get a valid expression for the conjugate of P.
    Then in what situation the conjugate can not be obtained by merely changing i to -i. An example please.
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  6. #6
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    Quote Originally Posted by Suvadip View Post
    Then in what situation the conjugate can not be obtained by merely changing i to -i. An example please.
    I don't believe that there are any such examples. This method will always work. In fact, conjugation is an automorphism of the field of complex numbers, so it commutes with addition, multiplication and division, and also with any function defined by means of a power series with real coefficients (such as the sinh and cosh functions in the above example).
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