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February 19th, 2011, 10:30 AM   #1
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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?
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February 19th, 2011, 11:18 AM   #2
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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.
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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 is a group under multiplication, but 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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