The condition satisfied by `omega` the imaginary ,cube root of unity is

If omega is the imaginary cube root of unity, then what is (2-omega+2omega^(2))^(27) equal to ?

The area of a quadrilateral whose vertices are 1,i,omega,omega^(2), where (omega!=1) is a imaginary cube root of unity, is

If (1+(omega)^2)^m = (1+(omega)^4)^m and omega is an imaginary cube root of unity, then least positive integral value of m is

Elements of a matrix A of order 10xx10 are defined as a_("ij")=omega^(i+j) (where omega is imaginary cube root of unity), then trace (A) of the matrix is

Elements of a matrix A of order 10xx10 are defined as a_("ij")=omega^(i+j) (where omega is imaginary cube root of unity), then trace (A) of the matrix is

Elements of a matrix A of order 10xx10 are defined as a_("ij")=omega^(i+j) (where omega is imaginary cube root of unity), then trace (A) of the matrix is

If omega be the imaginary cube root of unity then the value of omega^(241) will be