1. In the complex number range, the equation
$$
x^{2}+p x+1=0(p \in \mathbf{R})
$$

has two roots $\alpha, \beta$. If $|\alpha-\beta|=1$, then $p=$ $\qquad$
1. $\pm \sqrt{3}$ or $\pm \sqrt{5}$.
If the equation has real roots, then these two real roots are $\frac{ \pm \sqrt{5}+1}{2}$ and $\frac{ \pm \sqrt{5}-1}{2}$, at this time, $p= \pm \sqrt{5}$;

If the equation has no real roots, then these two complex roots are conjugate complex numbers, which are $\frac{ \pm \sqrt{3}+\mathrm{i}}{2}$ and $\frac{ \pm \sqrt{3}-\mathrm{i}}{2}$, at this time, $p= \pm \sqrt{3}$.