`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 (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 .

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

if ax^2+bx+c = 0 has imaginary roots and a+c lt b then prove that 4a+c lt 2b

If omega pm 1 is a cube root of unity, show that (a + b omega + c omega^(2))/(b + c omega + a omega^(2))+ (a + b omega + c omega^(2))/(c + a omega + b omega^(2)) = -1

If omega is an imaginary cube root of unity, then (1+omega-omega^2)^7 is equal to (a) 128omega (b) -128omega (c) 128omega^2 (d) -128omega^2

If omega is a complex cube root of unity, then (a+b omega+c omega^(2))/(c+a omega+b omega^(2))+(c+a omega+b omega^(2))/(a +b omega+c omega^(2))+(b+c omega+a omega^(2))/(b+c omega+a omega^(5))=

If omega ne 1 is a cube root of unity, then show that (a+bomega+comega^(2))/(b+comega+aomega^(2))+(a+bomega+comega^(2))/(c+aomega+bomega^(2))=1

If s intheta,costheta be the roots of a x^2+b x+c=0 , then prove that b^2=a^2+2ac.

If a+b+c=1, then prove that 8/(27a b c)>{1/a-1}{1/b-1}{1/c-1}> 8.

If 1, omega omega^(2) are the cube roots of unity show that (1 + omega^(2))^(3) - (1 + omega)^(3) = 0