Let f (z) be a polynomial (with complex coefficients) of degree n with no roots on the imaginary axis (i.e. the line z = ic where i is the imaginary unit and c is a real number). Let us define real polynomials P 0 (y) and P 1 (y) by f (iy) = P 0 (y) + iP 1 (y), respectively the real and imaginary parts of f on the imaginary line.