Browse · MATH Print → jmc algebra intermediate Problem Let z be a complex number such that z5=1 and z=1. Compute z+z1+z2+z21. Solution — click to reveal Since z5=1, z5−1=0, which factors as (z−1)(z4+z3+z2+z+1)=0.Since z=1, z4+z3+z2+z+1=0.Then z+z1+z2+z21=z2z3+z+z4+1=z2−z2=−1. Final answer -1 ← Previous problem Next problem →