A3

Part of 1989 Putnam

Problems(1)

Putnam 1989: A3 (Complex Numbers and Unit Modulus Proof)

Source: Looking for clever solutions!

Prove that all roots of 11z^{10} \plus{} 10iz^9 \plus{} 10iz \minus{}11 \equal{} 0 have unit modulus (or equivalent |z| \equal{} 1).

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