Putnam 1989: A3 (Complex Numbers and Unit Modulus Proof)
Source: Looking for clever solutions!
November 25, 2008
Putnamsearchalgebra proposedalgebra
Problem Statement
Prove that all roots of 11z^{10} \plus{} 10iz^9 \plus{} 10iz \minus{}11 \equal{} 0 have unit modulus (or equivalent |z| \equal{} 1).