  In this note we show that stable recovery of complex-valued signals
$x\in\mathbb{C}^n$ up to global sign can be achieved from the magnitudes of
$4n-1$ Fourier measurements when a certain "symmetrization and zero-padding" is
performed before measurement ($4n-3$ is possible in certain cases). For real
signals, symmetrization itself is linear and therefore our result is in this
case a statement on uniform phase retrieval. Since complex conjugation is
involved, such measurement procedure is not complex-linear but recovery is
still possible from magnitudes of linear measurements on, for example,
$(\Re(x),\Im(x))$.
