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

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

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)(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)(1+omega-omega^2)=4

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

A battery of 9V is connected in series with resistors of 0.2Omega , 0.3Omega , 0.4Omega , 0.5Omega and 12Omega , respectively. How much current would flow through the 12Omega resistor?

Find the derivative of sinx^2 w.r.t. x^2 .