complex numbers
Source: Ireland 1995
July 1, 2009
abstract algebratrigonometryalgebra unsolvedalgebra
Problem Statement
Let be complex numbers. Prove that if all the roots of the equation x^3\plus{}ax^2\plus{}bx\plus{}c\equal{}0 are of module , then so are the roots of the equation x^3\plus{}|a|x^2\plus{}|b|x\plus{}|c|\equal{}0.