Let z be a complex number such that z^5 + z^4 + 2z^3 + z^2 + z = 0. Find all possible values of |z|.
z=0 is an obvious solution|z|=0
Assume z≠0z5+z4+2z3+z2+z=0z4+z2=−z(z4+2z2+1)z(z2+1)=−(z2+1)2
if z2≠−1z=−(z2+1)z2+z+1=0z=−1±√−32=−12±i√32|z|=√14+34=1
if z2=−1z=±i|z|=1
