if `alpha_1`,`alpha_2`,.....`alpha_8` are the 8th roots of unity then:

If alpha_1,alpha_2....alpha_(n-1) are the nth roots of unity then show that (5-alpha_1)(5-alpha_2)(5-alpha_3)...(5-alpha_(n-1))= (5^n-1)/4

If 1,alpha_1,alpha_2,…..alpha_(n-1) are the n^(th) roots of unity then (1-alpha_1)(1-alpha_2)…..(1-alpha_(n-1))=

If alpha Is the fifth root of unity, then :

If 1,alpha_(1),alpha_(2)......alpha_(n-1) are n^(th) roots of unity then (1)/(1-alpha_(1))+(1)/(1-alpha_(2))+......+(1)/(1-alpha_(n-1))=

If 1,alpha_(1),alpha_(2),...,alpha_(n-1) are n^( th) roots of unity then (1)/(1-alpha_(1))+(1)/(1-alpha_(2))+....+(1)/(1-alpha_(n-1))=

1,alpha_(1),alpha_(2),..... alpha_(9), are the 10^(th) roots of unity. The product (2 alpha_(1)+1)(2 alpha_(2)+1)......(2 alpha_(9)+1) equals a reduced rational number (m)/(n) the value of m+n is

If 1, alpha,alpha^2.......alpha^(n-1) are the nth roots of unity then prove that (1-alpha)(1-alpha^2).....(1-alpha^(n-1))=n

If alpha Is the fifth root of unity,then :

If 1,alpha_1,alpha_2,…..alpha_(n-1) are the n^(th) roots of unity and n is an odd natural number then (1+alpha_1)(1+alpha_2)…..(1+alpha_(n-1))=

If 1,alpha,alpha^2,…...,alpha^(n-1) are the n^(th) roots of unity, then the value of (3-alpha)(3-alpha^2)…...(3-alpha^(n-1)) is