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Complex quadratic

  1. Sep 8, 2009 #1
    1. The problem statement, all variables and given/known data

    consider

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

    where a,b,c are unknown complex constants.

    find a formula for z in terms of a, b, c

    answer should be in the form "z = ..." where the ... does not contain any z or conj(z)


    2. Relevant equations

    I multiply the whole equation by z

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

    =

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

    =

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

    using the quadratic formula

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



    is this correct?

    thanks!



    3. The attempt at a solution
     
  2. jcsd
  3. Sep 8, 2009 #2

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    No, [itex]z\overline{z}=|z|^2\neq z^2[/itex] in general.

    Instead, take the complex conjugate of both sides of your original equation. That will give you two equations and two unknowns ([itex]z[/itex] and [itex]\overline{z}[/itex]) which you should know how to solve.
     
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