( r , ) denotes r( +i ) . If x=(1, ), y=(1, ) , z =(1, ) and x+y+z=0 then (2 - - )=

Step-by-step solution

Since (r, ) denotes r( +i ) aligned & So, x=(1, )= +i =e^ i & y=(1, )= +i =e^ i & and z=(1, )= +i =e^ i & Now, x+y+z=0 & x^3+y^3+z^3=3 x y z & x^2 y z + y^2 y z + z^2 x y =3 e^ 2 i e^ i e^ i + e^ 2 i e^ i e^ i + e^ 2 i e^ i e^ i =3 & e^ i(2 - - ) +e^ i(2 - - ) +e^ i(2 - - ) =3 aligned On comparing both sides (2 - - )=3