The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: complex numbers
Replies: 8   Last Post: Jan 31, 2007 7:33 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Michael Olea

Posts: 57
Registered: 12/13/04
Re: complex numbers
Posted: Jan 30, 2007 8:35 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

jennifer wrote:

> How would i evaluate the following:
> 1+2w+3w^2+...+nw^n-1, where w is an nth root of unity.
> apparently, the solution is: n(n+1)/2 if w= 1
> I don't know how they got this? Any hints please?

I can give you a hint for this part. When w=1 the sum is:


One hint is to notice the pattern:

1+n = n+1
2+(n-1) = n+1
3+(n-2)= n+1

And treat the cases n is odd and n is even separately.

Another way to look at it is to consider an nxn (square) matrix with 1's on
the main diagonal and upper triangle, and 0's on the lower triangle, and
figure out a formula for the number of 1's. For exmple, if n=5:


-- Michael

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.