If 1 , α 1 , α 2 , α 3 , α 4 are the roots of z 5 - 1 = 0 and ω is a cube root of unity then ( ω - 1 ) ω - α 1 ω - α 2 ω - α 3 ω - α 4 + ω is equal to

Step-by-step solution

∴   z 5 − 1 = ( z − 1 ) ( z − α 1 ) ( z − α 2 ) ( z − α 3 ) ( z − α 4 ) ∴ ω 5 − 1 = ( ω − 1 ) ( ω − α 1 ) ( ω − α 2 ) ( ω − α 3 ) ( ω − α 4 ) ( ω − 1 ) ( ω − α 1 ) ( ω − α 2 ) ( ω − α 3 ) ( ω − α 4 )   +   ω =   ω 5 − 1 +   ω =   ω 3 &