If `1,omega,omega^(2),...omega^(n-1)` are n, nth roots of
unity, find the value of `(9-omega)(9-omega^(2))...(9-omega^(n-1)).`

If omega is a non-real complex cube root of unity, find the values of (1+omega)(1+omega^(2) )(1+omega^(4))(1+omega^(8)) ...upto 2n factors

If 1,omega,omega^(2) are the cube roots of unity, then the roots of the equation (x-1)^(3)+8=0 are

If omega is a non-real complex cube root of unity, find the values of the following. (i) omega^(1999) (ii) omega^(998) (iii) ((-1+isqrt(3))/2)^(3n+2),ninNand i=sqrt(-1) (iv) (1+omega)(1+omega )^(2)(1+omega)^(4)(1+omega)^(8) ...upto 2n factors (v) ((alpha+betaomega+gammaomega^(2)+deltaomega^(2))/(beta+alphaomega^(2)+gammaomega+deltaomega))," where "alpha,beta,gamma,delta, in R (vi) 1*(2-omega)(2-omega^(2))+2*(3-omega)(3-omega^(2))+3*(4-omega)(4-omega^(2))+...+...+(n-1)*(n-omega)(n-omega^(2))

If a,b,c are distinct integers and omega(ne 1) is a cube root of unity, then the minimum value of |a+bomega+comega^(2)|+|a+bomega^(2)+comega| is

If omega(ne1) is a cube root of unity, then (1-omega+omega^(2))(1-omega^(2)+omega^(4))(1-omega^(4)+omega^(8)) …upto 2n is factors, is

With 1,omega,omega^(2) as cube roots of unity, inverse of which of the following matrices exists?

if omegaa n domega^2 are the nonreal cube roots of unity and [1//(a+omega)]+[1//(b+omega)]+[1//(c+omega)]=2omega^2 and [1//a+omega^2]+[1//b+omega^2]+[1//c+omega^2]=2omega^ , then find the value of [1//(a+1)]+[1//(b+1)]+[1//(c+1)]dot

If omega = z//[z-(1//3)i] and |omega| = 1 , then find the locus of z.

If omega is a cube root of unity but not equal to 1, then minimum value of abs(a+bomega+comega^(2)) , (where a,b and c are integers but not all equal ), is

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):}] where omega is the cube root of unit.