# Thread: Pls help me with this complex number problem

1. ## Pls help me with this complex number problem

If 1,w,w^2 are the cube roots of unity , then find the value of
(1+w)(1+w^2)(1+w^3)(1+w^4)(1+w^5)

2. Originally Posted by topsquark
Hint: $w^2 = w$. (First of all, can you prove this?)

-Dan
You mean $w^3=1$?

3. Originally Posted by math sucks
You mean $w^3=1$?
Ahem!

Um, yeah, what I wrote was kinda silly, wasn't it?

What I was trying to remember was this:
$w = a + ib \implies w^2 = a - ib$

But thinking about it a bit further I see there is a simpler way:
$w^4 = w$
and
$w^5 = w^2$

So your expression becomes
$2(1 + w)^2(1 + w^2)^2$

Now note that
$(1 + w)^2 = w$
and
$(1 + w^2)^2 = w^2$

-Dan