Thank you, now almost everything is clear for me except one thing. How do you know that:
?
I am sure you, as an expert, presented me it correctly, but i am just curious where it comes from. How do you know these identities? (they are not the common ones i think...)
I'm going to use for conjugate, it's easier to use (see below).
You already have that .
So .
But you also have that (it's a standard result, but simple to prove).
So .
Multiply this out, you get
.
But as (which you should be able to prove, it's very straightforward), this works out as
.
The result follows from .