Find the value of : `|(1,omega^3,omega^2),(omega^3,1,omega),(omega^2,omega,1)|`

Find the value of : |(1,omega,omega^2),(omega,omega^2,1),(omega^2,1,omega)|

If omega is a complex cube root of unity, then find the value of |(1,omega),(-omega, omega)| .

If omega be an imaginary cube root of unity, prove that (1-omega+omega^2)(1+omega-omega^2)=4

If omega be an imaginary cube root of unity, prove that (1-omega)(1-omega^2)(1-omega^4)(1-omega^8)=9

If omega be an imaginary cube root of unity, prove that (1-omega+omega^2)^4+(1+omega-omega^2)^4=-16

If omega be an imaginary cube root of unity, prove that omega^4+omega^8+1/omega+1/omega^2=-2

Find the derivate of : y = (cos ^-1x)^2 w.r.t. cos^-1 x

Judge the equivalent resistance when the following are connected in parallel ----- 1Omega and 10^6Omega , 1Omega and 10^3Omega , and 10^6Omega .