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Generalized complex circle

  1. Mar 30, 2010 #1
    1. The problem statement, all variables and given/known data

    Let have the problem to find the complex generalized cirlce of radius r

    2. Relevant equations

    [tex]|z-c|^2 = r^2 [/tex]

    3. The attempt at a solution

    hvor r is the radius and c the center..

    by expanding the above

    [tex]z\overline{z} - z\overline{c} - \overline{z}c + c\overline{c} -r^2 = 0[/tex]

    I know that if I multiply with a real number when I can get a more pretty expression, but what as is my motivation to do this?

  2. jcsd
  3. Mar 30, 2010 #2


    User Avatar
    Homework Helper

    You mean you want to prove that

    |z-c|=r is a circle?

    if so then just recall z=x+iy and that c is also a complex number.
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