In: Advanced Math
Question 1:
a) What are the complex roots of x^8-1 ?
b) What are the irreducible factors of f(x)=x^8-1 in R[x]?
c) What are the irreducible factors of f(x)=x^8-1 in Q[x]?
(a) We have to find out complex root of
now
......................................(1)
Thus we have
also,
Again we have
where n be integer
so we have n=0,1,2,3
when n=0 then
When n=1
when n=2
when n=3
Hence we got the complex root are
and
(b) Form (1) we seen that so the irreducable factor of in is and
(c) Here also irreduciable factor of in is and