[math-fun] H.Brady's |exp(ix)|=1 request

What you want is exp(ix) =approx= (A+Bi) / (C+Di) where A,B,C,D are real polynomials in x with A^2+B^2=C^2+D^2. For example if A=C=even, B=-D=odd, this is achieved and also exp(-ix)=conjugate(exp(ix)) is always satisfied.