# Complex Numbers Problem

• Jan 17th 2008, 09:04 AM
flaming
Complex Numbers Problem
Hey

can some one tel me how do i go about solving this question

Let m be a positive fixed interger and l be an integer that is not divisible by m

prove

1 + w^l + w^2l + .... + w^(m-1)l = 0

all the w's have subscript "m".

Thanks
• Jan 17th 2008, 09:07 AM
ThePerfectHacker
Quote:

Originally Posted by flaming

1 + w^l + w^2l + .... + w^(m-1)l = 0

I assume that $\omega = e^{2\pi i/m}$

Then, $\omega^l = e^{2\pi il/m}\not = 1$ since $m\not | l$.

Now use geometric sum, $\frac{1 - (\omega^l )^{m}}{1-\omega^l} = 0$.