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Please very my solution: complex analysis

  1. Sep 9, 2009 #1
    1. The problem statement, all variables and given/known data

    1) consider

    [tex] az - b*conj(z) + c = 0 [/tex]

    where a,b,c are complex unknown constans

    express z in terms of a,b,c

    2. Relevant equations



    3. The attempt at a solution


    ok so i took the conjugate of the original equation to get a second equation:

    [tex] a*conj(z) - b*z + c = 0 [/tex]

    so my two equations are

    1) [tex] az - b*conj(z) + c = 0 [/tex]

    2) [tex] a*conj(z) - b*z + c = 0 [/tex]

    in order to get rid of the conj(z) i multiply the top by a and bottom by b

    1) [tex] a^2z - ab*conj(z) + ac = 0 [/tex]

    2) [tex] ab*conj(z) - b^2z + bc = 0 [/tex]

    i simply add and simplify and my answer is

    [tex] z = -\frac {a+b}{a^2-b^2} * c [/tex]

    does this seem correct?
     
  2. jcsd
  3. Sep 9, 2009 #2
    If the problem states that a,b,c are complex constants, then when you conjugate the entire equation, you need to conjugate these constants as well.
     
  4. Sep 9, 2009 #3
    ok, woul the final answer just be my answer with conjugate signs above all the constants?
     
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