[" Let "omega=e^(i pi/3)*8ca,6,C,x,y,z" lee Non "20times0" somplens "],[" number awh that "],[a+6+c=x],[[a+6w+cw^(2)=y],[a+6w^(2)+cw=2]]

Let omega=e^((i pi)/(3)) and a,b,c,x,y,z be non-zero complex numbers such that a+b+c=x,a+b omega+c omega^(2)=y,a+b omega^(2)+c omega=z Then,the value of (|x|^(2)+|y|^(2)|+|y|^(2))/(|a|^(2)+|b|^(2)+|c|^(2))

Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numbers such that a+b+c = x, a + bomega + comega^2 = y, a + bomega^2 + comega = z .Then, the value of (|x|^2+|y|^2|+|z|^2)/(|a|^2+|b|^2+|c|^2)

Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numbers such that a+b+c = x, a + bomega + comega^2 = y, a + bomega^2 + comega = z .Then, the value of (|x|^2+|y|^2|+|y|^2)/(|a|^2+|b|^2+|c|^2)

Let omega= e^((ipi)/3) and a, b, c, x, y, z be non-zero complex numbers such that a+b+c = x, a + bomega + comega^2 = y, a + bomega^2 + comega = z .Then, the value of (|x|^2+|y|^2|+|y|^2)/(|a|^2+|b|^2+|c|^2)

Find x,y,z and w such that [(x-y,2z+w),(2x-y,2x+w)]=[(5,3),(12,15)]

If w be a imaginary cube root of uniyt and a+b+c=0 then show that (a+bw+cw^2)^3+(a+bw^2+cw)^3=27abc