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)
Ahem!
Um, yeah, what I wrote was kinda silly, wasn't it?
What I was trying to remember was this:
$\displaystyle w = a + ib \implies w^2 = a - ib$
But thinking about it a bit further I see there is a simpler way:
$\displaystyle w^4 = w$
and
$\displaystyle w^5 = w^2$
So your expression becomes
$\displaystyle 2(1 + w)^2(1 + w^2)^2$
Now note that
$\displaystyle (1 + w)^2 = w$
and
$\displaystyle (1 + w^2)^2 = w^2$
-Dan