May 6th, 2019, 04:14 PM  #11 
Newbie Joined: Oct 2017 From: Egypt Posts: 15 Thanks: 0 
Okay, but what if the given was only three brackets? 59934030_653367038444064_1692238877223288832_n.jpg Last edited by yoyo145; May 6th, 2019 at 04:42 PM. 
May 6th, 2019, 04:54 PM  #12 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
If the number of factors is odd, the righthand side will need to involve ω.

May 6th, 2019, 04:56 PM  #13 
Newbie Joined: Oct 2017 From: Egypt Posts: 15 Thanks: 0  The number of factors is even: 2n
Last edited by skipjack; May 7th, 2019 at 02:28 AM. 
May 7th, 2019, 02:27 AM  #14 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
I took "only three brackets" to mean "only three factors", which won't arise (because 2n is even).

May 7th, 2019, 02:37 AM  #15  
Newbie Joined: Oct 2017 From: Egypt Posts: 15 Thanks: 0  Quote:
prove that: 59934030_653367038444064_1692238877223288832_n.jpg =1 Last edited by yoyo145; May 7th, 2019 at 02:55 AM.  
May 7th, 2019, 03:01 AM  #16 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
What new problem? For problem (8), consider the factors in successive pairs, as already described. Can you try it for yourself and post your work?

May 7th, 2019, 03:20 AM  #17 
Newbie Joined: Oct 2017 From: Egypt Posts: 15 Thanks: 0  Okay, but really I don't understand why 2n factors means successive pairs. When I read it, I think the question mean to 8 factor or to 10 factors.
Last edited by skipjack; May 7th, 2019 at 06:47 AM. 
May 7th, 2019, 06:57 AM  #18 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
The question doesn't specify successive pairs. I suggested successive pairs because that's a convenient way to find the product.

May 7th, 2019, 07:13 AM  #19 
Newbie Joined: Oct 2017 From: Egypt Posts: 15 Thanks: 0 
So your answer is not general because if you get three factors we will not figure out the right answer. Please check my proof. Last edited by skipjack; May 7th, 2019 at 07:18 AM. 
May 7th, 2019, 07:17 AM  #20 
Global Moderator Joined: Dec 2006 Posts: 20,921 Thanks: 2203 
There can't be just three factors because it is stated that there are 2n factors.


Tags 
(1ω)(1ω^2), cube roots of unity, cubic roots of unity, problem, yahia kamal 
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