[" If "omega" is an imaginary cube root of unity such "],[(1)/(a+omega)+(1)/(b+varphi)+(1)/(c+omega)=2 omega^(2)],[(1)/(a+omega^(2))+(1)/(b+omega^(2))+(1)/(c+omega^(2))=2 omega" then the valu "],[1" can be equal to "]

If omega be an imaginary cube root or unity, prove that (1)/(1+2 omega)-(1)/(1+ omega)+(1)/(2+omega)=0

If omega be an imaginary cube root of unity, show that: 1/(1+2omega)+ 1/(2+omega) - 1/(1+omega)=0 .

If omega be an imaginary cube root of unity, show that: 1/(1+2omega)+ 1/(2+omega) - 1/(1+omega)=0 .

If omega ne 1 is a cube root of unity such that : (1)/(a+omega)+(1)/(b+omega)+(1)/(c+omega)=2omega^(2) and (1)/(a+omega^(2))+(1)/(b+omega^(2))+(1)/(c+omega^(2))=2omega , then the value of (1)/(a+1)+(1)/(b+1)+(1)/(c+1) is :

If omega_(1) is complex cube root of that (1)/(a+omega)+(1)/(b+omega)+(1)/(c+omega)=2 omega^(2) and (1)/(a+omega^(2))+(1)/(b+omega^(2))+(1)/(c+omega^(2))=2 omega then the value of (1)/(a+1)+(1)/(b+1)+(1)/(c+1)=

If omega_(1) is complex cube root of that (1)/(a+omega)+(1)/(b+omega)+(1)/(c+omega)=2 omega^(2) and (1)/(a+omega^(2))+(1)/(b+omega^(2))+(1)/(c+omega^(2))=2 omega then the value of (1)/(a+1)+(1)/(b+1)+(1)/(c+1)=

If omega is an imaginary cube root of unity, then the value of (1)/(1+2omega)+(1)/(2+omega)-(1)/(1+omega) is :

If omega is an imaginary cube root of unity, then the value of (1+ omega- omega^(2))(1- omega + omega ^(2)) is-

If omega is an imaginary cube root of unity then (1 + omega-omega^2)^5 + (1-omega+omega^2)^5 = ?