Home
Class 12
MATHS
If omega!=1 is a cube root of unity a...

If `omega!=1` is a cube root of unity and `x+y+z!=0,` then prove that `|x/(1+omega)y/(omega+omega^2)z/(omega^2+1)y/(omega+omega^2)z/(omega^2+1)x/(1+omega)(z z)/(omega^2+1)x/(1+omega)y/(omega+omega^2)|=0` if `x=y=z`

Promotional Banner

Similar Questions

Explore conceptually related problems

if omega!=1 is cube root of unity and x+y+z!=0(x)/(1+omega),(y)/(omega+omega^(2)),(z)/(omega^(2)+1)(y)/(omega+omega^(2)),(z)/(omega^(2)+1),(x)/(1+omega)(z)/(omega^(2)+1),(x)/(1+omega),(y)/(omega+omega^(2))]|=0 if

If omega is non-real cube roots of unity,then prove that |(x+y omega+z omega^(2))/(xw+z+y omega^(2))|=1

If omega is cube roots of unity, prove that {[(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega)]+[(omega,omega^2,1),(omega^2,1,omega),(omega,omega^2,1)]} [(1),(omega),(omega^2)]=[(0),(0),(0)]

If omega is a cube root of unity , then |(x+1 , omega , omega^2),(omega , x+omega^2, 1),(omega^2 , 1, x+omega)| =

If omega is a cube root of unity, then for polynomila is |(x + 1,omega,omega^(2)),(omega,x + omega^(2),1),(omega^(2),1,x + omega)|

If omega!=1 is a cube root of unity and Delta=|(x+omega^(2),omega,1),(omega,omega^(2),1+x),(1,x+omega,omega^(2))|=0 then value of x is

If omega is an imaginary cube root of unity, then a root of equation |(x+1,omega,omega^2),(omega,x+omega^2,1),(omega^2,1,x+2)|=0,can be

If omega is a complex cube root of unity, then a root of the equation |(x +1,omega,omega^(2)),(omega,x + omega^(2),1),(omega^(2),1,x + omega)| = 0 , is