# FP3 nth roots of unity question

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Thread starter 7 years ago
#1
if w=(2pi/5)i simplify (1-w)(1-w2)(1-w3)(1-w4)

the answer is 5

I tried expanding and figured that was a waste of time

I have a feeling the answer is obvious please help
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7 years ago
#2
(Original post by physics4ever)
if w=(2pi/5)i simplify (1-w)(1-w2)(1-w3)(1-w4)

the answer is 5

I tried expanding and figured that was a waste of time

I have a feeling the answer is obvious please help
There's probably better ways of doing it, but here we go:

Note that and that and so (since )

Expand and separately (and noting my first point, simplify both expressions), and then multiply them together. You will end up with and terms but they can be simplified as well. Group bits together that look useful, e.g. and see where you end up
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