Homework Help: Generalized complex circle

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?

/Susanne