Complex Analysis Homework: Need Help Showing Statement is 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.