If $|z_1 + z_2| = |z_1 - z_2|$,then the difference in the amplitudes of $z_1$ and $z_2$ is

If $z_1$ and $z_2$ are two distinct complex numbers such that $\left|\frac{z_1-2 z_2}{\frac{1}{2}-z_1 \bar{z}_2}\right|=2$,then:

The complex number $\frac{1 + 2i}{1 - i}$ lies in which quadrant of the complex plane?

If $z$ is a complex number such that $\frac{z-i}{z-1}$ is purely imaginary,then the minimum value of $|z-(3+3i)|$ is:

Let the point $P$ represent $z=x+iy$, where $x, y \in \mathbb{R}$, in the Argand plane. Let the curves $C_1$ and $C_2$ be the loci of $P$ satisfying the conditions $(i)$ $\frac{2z+i}{z-2}$ is purely imaginary and $(ii)$ $\operatorname{Arg}\left(\frac{z+i}{z+1}\right)=\frac{\pi}{2}$, respectively. Then the point of intersection of the curves $C_1$ and $C_2$, other than the origin, is

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 $a^2+b^2=$