If α(≠1) is a fifth root of unity and β(≠1) is a fourth root of unity thenz=(1+α)(1+β)1+α21+β21+α31+β3 equals

As β≠1 is a fourth root of unity,β4=1⇒(1−β)1+β+β2+β3=0As            β≠1,1+β+β2(1+β)=0⇒             (1+β)1+β2=0∴               z=0