7. Given that the modulus of the complex number $z$ is 1, if when $z=z_{1}$ and $z=z_{2}$, $|z+1+\mathrm{i}|$ attains its maximum and minimum values respectively, then $z_{1}-z_{2}=$ $\qquad$ .
Solving by plotting, we get $z_{1}=\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2} \mathrm{i}, z_{2}=-\frac{\sqrt{2}}{2}-\frac{\sqrt{2}}{2} \mathrm{i}$, so $z_{1}-z_{2}=\sqrt{2}(1+\mathrm{i})$.