1. The modulus of the difference between the two roots of the equation $x^{2}+a x+4=0$ equals $a$, then $a=$
1. $a=2 \sqrt{2}$

If $\Delta \geqslant 0$, i.e., $|a| \geqslant 4, \left|x_{1}-x_{2}\right|=\sqrt{a^{2}-16}=a$ leads to a contradiction!
If $\Delta<0$, i.e., $|a|<4, \left|x_{1}-x_{2}\right|=\sqrt{16-a^{2}}=a, \Rightarrow a=2 \sqrt{2}$.