Four, the trajectory equation of a moving point $z_{1}$ in the complex plane is $\left|z_{1}-z_{0}\right|=\left|z_{1}\right|, z_{0}$ is a fixed point, $z_{0} \neq 0$, another moving point $z$ satisfies $z_{1} z=-1$, find the trajectory of point $z$, and indicate its shape and position on the complex plane.
A circle with the point $Z=0$ removed
Four, 【Analysis and Solution】From $z_{1} z=1$, we get $z_{1}=-\frac{1}{z}$. Substituting into $\left|z_{1}-z_{0}\right|=\left|z_{1}\right|$, we get $\left|\frac{1}{z}+z_{0}\right|=\left|\frac{1}{z}\right|$. Multiplying both sides by $\left|\frac{z}{z_{0}}\right|$, we get $\left|z+\frac{1}{z_{0}}\right|=\frac{1}{\left|z_{0}\right|}$. This is a circle with center $-\frac{1}{z_{0}}$ and radius $\left|\frac{1}{z_{0}}\right|$, and since $z \neq 0$, otherwise $z_{1} z=0 \neq-1$, therefore, the required trajectory is the curve of this circle with the point $z=0$ removed.