Question

Find the product of the nth root of 1. I got either one or infinity... of course I'm not entirely sure what the question is asking...

Answer 1

... you lost me at k ._.

Answer 2

So is it one...? I don't understand a word on that page, and don't think I learned about roots of unity...

Answer 3

I don't know what math this is... I was just placed in my school's Math Team and have to do the homework, but so far I've missed about 2-3 weeks of class since I was just put in it...

Answer 4

"In mathematics, a root of unity, or de Moivre number, is any complex number that equals 1 when raised to some integer power n."-Wikipedia. So all I understand from this is that the answer is one...?

Answer 5

I sucked at Algebra I, aced Geometry, was put into an advanced Trig and Algebra II class and got a 76, but then I became good at Algebra I... on Regents level I got an 89 (in Trig/AII, in A I I'm now almost at a 100 on Regents level I think). So that's the level I'm at when it comes to math.

Answer 6

Yes... and specifically the New York system lol

Answer 7

Basically, I'm great at Algebra I and Geometry, okay at Trig and Algebra II, and I haven't done any math beyond that. That make any more sense?

Answer 8

I'm 17

Answer 9

Last year of high school

Answer 10

Ah... so, I'm looking at the equation. I don't know n or k, but you told me that k is the roots of unity, which is anything that equals 1 when raised to n... would that make n = 0? O_o

Answer 11

I don't understand the "by induction" part that the person is asking on the non-Wiki page..

Answer 12

Wait

Answer 13

Are the roots of unity imaginary?

Answer 14

i will try to keep this as simple as possible:
let x be the variable to represent n'th root of 1
\(x=1^{(1/n)}\)
raising to n'th power
\(x^n=1 \\ x^n-1=0\)
is your polynomial equation.

Now we use a property that the product of roots of general equation \(Ax^n+Bx^{n-1}+Cx^{n-2}+....N=0\) is \((-1)^n\) times the constant co-efficient.
So the product of roots of x^n-1 = 0 will be
\((-1)^n (-1)=(-1)^{n+1}\)

this is your product of n'th root of 1.
hope this makes some sense.Ask if there is doubt in any step.

Answer 15

Is that the answer then, or is there more that needs to be solved?

Answer 16

that is the answer (-1)^{n+1}

Answer 17

I'm a little lost at the property of the product of the roots... where did you get (-1)^n? Otherwise, I think I understand the rest.

Answer 18

its a general formula , it can be proved, but i donno the best way to prove it.
the property is listed here, where u have sum of roots, product of roots and other formulas....just go through it....
http://en.wikipedia.org/wiki/Vieta%27s_formulas

Answer 19

Okay! Thank you very much! You have been so helpful today! :)

Answer 20

welcome very much \(\ddot\smile\)