Let $|z_1 - 8 - 2i| \leq 1$ and $|z_2 - 2 + 6i| \leq 2$,where $z_1, z_2 \in \mathbb{C}$. Then the minimum value of $|z_1 - z_2|$ is:

The minimum value of $|z-1|+|z-5|$ is

If a complex number $z$ satisfies $|z^2-1|=|z|^2+1$,then $z$ lies on

$z=x+iy$ and the point $P$ represents $z$ in the Argand plane. If the amplitude of $\left(\frac{2z-i}{z+2i}\right)$ is $\frac{\pi}{4}$,then the equation of the locus of $P$ is

If ${z_1} = 10 + 6i$,${z_2} = 4 + 6i$ and $z$ is a complex number such that $\text{amp}\left( \frac{z - z_1}{z - z_2} \right) = \frac{\pi}{4}$,then the value of $|z - 7 - 9i|$ is equal to

If $z$ is a complex number such that $|z+4| \geq 3$,then the smallest value of $|z+3|$ is