If $a$ and $b$ are the least and the greatest values respectively of $|z_1+z_2|$,where $z_1=12+5i$ and $|z_2|=9$,then $a^2+b^2=$

If $a, b, c$ and $u, v, w$ are complex numbers representing the vertices of two triangles such that $c = (1 - r)a + rb$ and $w = (1 - r)u + rv$,where $r$ is a complex number,then the two triangles

If $z$ is a complex number,then the curves $|z|=1$,$|z-2|=1$,and $|z-1|=0$ have a common point at

The complex number $z$ satisfying the equation $|z-i|=|z+1|=1$ is

If $z$ and $\omega$ are two non-zero complex numbers such that $|z \omega|=1$ and $\operatorname{Arg}(z) - \operatorname{Arg}(\omega) = \frac{\pi}{2}$,then $\bar{z} \omega =$

If $z, iz$ and $z + iz$ are the vertices of a triangle whose area is $2$ units,then the value of $|z|$ is