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## Homework Statement

Show that the equation [tex]|z - z_0| = R[/tex] of a circle, centered at [tex]z_0[/tex] with radius R, can be written

[tex]|z|^2 - 2Re(z\bar{z_0}) + |z_0|^2 = R^2[/tex].

## Homework Equations

## The Attempt at a Solution

Honestly, I have no clue where to start with this problem. I know that I need to reduce the given equation to the basic equation of a circle but I do not know where to start.

I also know that the two equations are almost exact except for the [tex]- 2Re(z\bar{z_0})[/tex] which should reduce to zero somehow I just do not know where to start.

I know [tex]Re(z) = Re(\bar{z}) = Re\frac{(z + \bar{z})}{2} = x[/tex]. Is this where I start?