Can you please help me to solve this very difficult exercice (for me).
n is an integer (n>0) ; z is a complex such |z|=1
I have to show that
I try to write
and the sum is equal to
But it doesn't work
Thanks for any help.
Let us notice that this you get the same number whether you use
in this question, since
commutes with complex conjugation.
So it is sufficient to show that:
by the triangle inequality, we have:
and I think from here it's not too hard to get this to be
, but I'm in a rush, so I cannot finish right now.