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 February 19th, 2011, 10:30 AM #1 Newbie   Joined: Feb 2011 Posts: 13 Thanks: 0 Roots of unity Can anyone help me with this? How can I prove that the nrth roots of unity (the set of all solutions to the equation x^n=1) form a group of order n. What are the generators?
 February 19th, 2011, 11:18 AM #2 Senior Member   Joined: Nov 2010 From: Staten Island, NY Posts: 152 Thanks: 0 Re: Roots of unity The roots of unity are a subset of the complex numbers containing 1. Since the complex numbers are a group under multiplication you need only show that when you multiply 2 roots of unity you get another root of unity. That is a simple computation.
February 19th, 2011, 01:20 PM   #3
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Re: Roots of unity

Quote:
 Originally Posted by DrSteve Since the complex numbers are a group under multiplication you need only show that when you multiply 2 roots of unity you get another root of unity.
Remember that $\mathbb{C}\setminus\{0\}$ is a group under multiplication, but $\mathbb{C}$ itself is not. You should therefore also show that 0 cannot be a root of unity - this is not difficult, though...

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