Very elegant, thank you! As a simple case, |z'/z|=1, for any complex number z, so in particular, |z'/z|=1 for any _Gaussian integer_ z. At 05:47 AM 8/11/2013, Warren D Smith wrote:

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.