If x, y and z are the cube roots of unity, then what is the value of x y+y z+z x ?

Step-by-step solution

x, y, z are cube root of unity aligned & Let, x=1, y=w, z=w^2 & Value of x y+y z+z x & =1 w+w w^2+w^2 1 & =w+w^3+w^2 aligned [ array l w^3=1 1+w+w^2=0 array ] aligned & =w+1+w^2 & =1+w+w^2=0 aligned