physics4ever
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Report Thread starter 7 years ago
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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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Blazy
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Report 7 years ago
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(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  w^5 = 1 and that  1-w^5 = (1-w)(1+w+w^2+w^3+w^4) and so  1+w+w^2+w^3+w^4 = 0  (since  w \neq 1 )

Expand  (1-w)(1-w^4) and  (1-w^2)(1-w^3) separately (and noting my first point, simplify both expressions), and then multiply them together. You will end up with  w^6 and  w^7 terms but they can be simplified as well. Group bits together that look useful, e.g.  1+w+w^2+w^3+w^4 = 0  and see where you end up
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