Complex numbers|Cube roots of unity

To find the roots of any Complex Number, Cube roots of Unity

Problems based on Euler's form, To find roots of any Complex-Number, Cube - roots of unity.

If omega is a complex non-real cube root of unity, then omega satisfies which one of the following equations ?

If alpha,beta are the complex cube roots of unity then alpha^(100)+beta^(100)+(1)/(alpha^(100)xx beta^(100))=

If alpha and beta are the complex cube roots of unity, then what is the vlaue of (1+alpha)(1+beta)(1+alpha^(2))(1+beta^(2)) ?