Polarity inversion in frequency domain (polar coordinates)
This is really basic, but here's how it works. If $X(\omega)$ is the Fourier transform of $x(t)$, then we obviously have

$$\mathcal{F}\{-x(t)\}=-\mathcal{F}\{x(t)\}=-X(\omega)$$

Furthermore,

$$X(\omega)=|X(\omega)|e^{j\phi(\omega)}$$

where $\phi(\omega)$ is the phase. From this we have

$$-X(\omega)=-|X(\omega)|e^{j\phi(\omega)}=|X(\omega)|e^{j(\phi(\omega)\pm\pi)}$$

because $e^{\pm j\pi}=-1$. So Jazzmaniac's comment that the phase needs to be shifed by $\pm \pi$ (or any odd multiple of $\pi$ for that matter) is of course correct.