Proving a complex analysis statement true

[asi123]

Homework Statement

Hey guys.

I have this problem, I need to show that it's true and I don't have a clue.
I tried to do like alpha = x+yi but it got me nowhere, any ideas?

Thanks.

Homework Equations

The Attempt at a Solution

 

[yyat]

Try to show that

$$|1-\bar{\alpha}z|^2=|z-\alpha|^2$$ if and only if $$|z|^2=1$$

and keep in mind that

$$|w|^2=w\bar{w}$$.

 

[asi123]

Try to show that

$$|1-\bar{\alpha}z|^2=|z-\alpha|^2$$ if and only if $$|z|^2=1$$

and keep in mind that

$$|w|^2=w\bar{w}$$.

Thanks.