39as given in the question, they are n th roots of unity
If 1,α1,α2,...,αn-1 are nth roots of unity ,
then value of (1+α1(1+α2)...(1+αn-1)
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8 Answers
11u get
1+( α1+α2+.........αn-1)+( α1.α2+.........αn-2.αn-1)+.........( α1.α2........αn-2.αn-1)
we also know that
α1.α2.α3......αn-1=1
and
1+α1+α2.......+αn-1=0
and
αn=1
now the question is urs.
moreover ucan also put n=3 and solve[1]
1and how do we find sum of roots taken 2 at a time, sum of roots taken 3 at a time, etc?
341Hint: 1+z+z^2+...+z^{n-1} = (z- \alpha_1)(z-\alpha_2)...(z-\alpha_{n-1})
62put z=___ (Fill in the blank)
in prophet sir's hint
To complete the proof.