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 Post subject: hard complex inequalityPosted: Wed, 5 Oct 2011 14:48:47 UTC

Joined: Wed, 28 Sep 2011 15:35:23 UTC
Posts: 8
Hello.
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 et
so
and the sum is equal to
But it doesn't work

Thanks for any help.

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 Post subject: Re: hard complex inequalityPosted: Wed, 5 Oct 2011 16:17:48 UTC
 Moderator

Joined: Wed, 30 Mar 2005 04:25:14 UTC
Posts: 12074
Location: Austin, TX
jason32 wrote:
Hello.
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 et
so
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 or in this question, since commutes with complex conjugation.

This means

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.

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