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

What is omega^(100)+omega^(200)+omega^(300) equal to, 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 ?

The value of (1-omega+(omega)^2)(1-(omega)^2+omega)^6 , where omega,(omega)^2 are the cube roots of unity is

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

If A =({:( 1,1,1),( 1,omega ^(2) , omega ),( 1 ,omega , omega ^(2)) :}) where omega is a complex cube root of unity then adj -A equals

sqrt(-1-sqrt(-1-sqrt(-1oo))) is equal to (where omega is the imaginary cube root of unity and i=sqrt(-1))

sqrt(-1-sqrt(-1-sqrt(-1oo))) is equal to (where omega is the imaginary cube root of unity and i=sqrt(-1))