The value of `w^2+w^5+w^8+3w+3` is, (where `w` is a non real cube root of unity)

Find the value of w^4+w^6+w^8 , if w is a complex cube root of unity.

Find the value of |{:(" "1+i," "i omega," "i omega^(2)),(" "i omega," "i omega^(2)+1," "i omega^(3)),(i omega^(2), i omega^(3), " "i omega^(4)+1):}| , where omega is a non real cube root of unity and i = sqrt(-1) .

The value of Sigma_(k=1)^(99)(i^(k!)+omega^(k!)) is (where, i=sqrt(-1) amd omega is non - real cube root of unity)

Prove that |[1,w^2,w^2],[w^2,1,w],[w^2,w,1]|=-3w where w is a cube root of unity.

Prove that (1+w)(1+w^2)(1+w^4)(1+w^8)=1 where w is the imagination cube root of unity.

Show that det ([1,omega,omega^(2)omega,omega^(2),1omega,omega^(2),1omega^(2),1,omega])=0 where omega is the non-real cube root of unity =0 where omega is

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