Generalized complex circle

Susanne217

Homework Statement

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

Homework Equations

$$|z-c|^2 = r^2$$

The Attempt at a Solution

hvor r is the radius and c the center..

by expanding the above

$$z\overline{z} - z\overline{c} - \overline{z}c + c\overline{c} -r^2 = 0$$

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