find the value of `|[1,1,1],[1,omega^(2),omega],[1,omega,omega^(2)]|` where `omega`is a cube root of unity

Evaluate: | (1, 1, 1), (1, omega^2, omega), (1, omega, omega^2)| (where omega is an imaginary cube root unity).

Evaluate |(1,omega,omega^2),(omega,omega^2,1),(omega^2,omega,omega)| where omega is cube root of unity.

What is the value of |{:(" "1-i," "omega^(2)," "-omega),(" "omega^(2)+i," "omega," "-i),(1-2i-omega^(2),omega^(2)-omega,i-omega):}| , where omega is the cube root of unity ?

What is the value of |(1-i, omega^2,-omega), (omega^2+i,omega,-i), (1-2i-omega^2,omega^2-omega,i-omega)|, where omega is the 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 area of a quadrilateral whose vertices are 1,i,omega,omega^(2), where (omega!=1) is a imaginary cube root of unity, is

What is sqrt((1+_(omega)^(2))/(1+_(omega))) equal to, where omega is the cube root of unity ?