`omega` is an imaginary root of unity. Prove that If `a+b+c=0,` then prove that `(a+bomega+comega^2)^3+(a+bomega^2+comega^)^3=27a b cdot`

omega is an imaginary root of unity. Prove that If a+b+c = 0 then prove that (a + bomega + comega^(2))^(3)+(a+bomega^(2) + comega)^(3) = 27abc .

omega is an imaginary root of unity. Prove that (i) ( a + bomega + comega^(2))^(3) + (a+bomega^(2) + comega)^(3) = (2a-b-c)(2b -a -c)(2c -a-b) (ii) If a+b+c = 0 then prove that (a + bomega + comega^(2))^(3)+(a+bomega^(2) + comega)^(3) = 27abc .

omega is an imaginary root of unity. Prove that (a+bomega+comega^2)^3+(a+bomega^2+comega^)^3 =(2a-b-c)(2b-a-c)(2c-a-b)dot

If omega is an imaginary cube root of unity then the equation whose roots are 2omega + 3omega^(2) and 2omega^(2) + 3omega is

If omega is an imaginary cube root of unity, then the value of |(a,b omega^(2),a omega),(b omega,c,b omega^(2)),(c omega^(2),a omega,c)| , is

If a+b+c=0 and omega,omega^2 are imaginary cube roots of unity, then (a+bomega+comega^2)^3+(a+bomega^2+comega)^3= 3abc (b) 6abc (c) 9 abc (d) 27 abc

If omega be an imaginary cube root of unity, show that (a+bomega+comega^2)/(aomega+bomega^2+c) = omega^2

If a+b+c=0 and omega,omega^2 are imaginary cube roots of unity, then (a+bomega+comega^2)^2+(a+bomega^2+comega)^3= 3abc (b) 6abc (c) 9 abc (d) 27 abc

If omega is an imaginary fifth root of unity, then find the value of loe_2|1+omega+omega^2+omega^3-1//omega|dot

If omega is an imaginary fifth root of unity, then find the value of log_2|1+omega+omega^2+omega^3-1//omega|dot