Mathematics - Complex Number Question with Solution | TestHub

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 $\frac{|x{|}^2+|y{|}^2+|z{|}^2}{|a{|}^2+|b{|}^2+|c{|}^2}$ is