If $z$ is a complex number such that $z^2 = (\bar{z})^2$,then

Let $w$ $(Im\, w \neq 0)$ be a complex number. Then the set of all complex numbers $z$ satisfying the equation $w - \overline{w}z = k(1 - z)$, for some real number $k$, is

Let $\omega = z \bar{z} + k_1 z + k_2 i z + \lambda(1 + i)$,where $k_1, k_2 \in R$. Let $\operatorname{Re}(\omega) = 0$ be the circle $C$ of radius $1$ in the first quadrant touching the line $y = 1$ and the $y$-axis. If the curve $\operatorname{Im}(\omega) = 0$ intersects $C$ at $A$ and $B$,then $30(AB)^2$ is equal to $.......$.

The equation $|z+1-i|=|z-1+i|$ represents a (where $z$ is a complex number)

Match the statements in column-$I$ with those in column-$II$.
[Note: Here $z$ takes the values in the complex plane and $\operatorname{Im} z$ and $\operatorname{Re} z$ denote,respectively,the imaginary part and the real part of $z$]

column-$I$	column-$II$
$(A)$ The set of points $z$ satisfying $|z-i|z||=|z+i|z||$ is contained in or equal to	$(p)$ an ellipse with eccentricity $\frac{4}{5}$
$(B)$ The set of points $z$ satisfying $|z+4|+|z-4|=10$ is contained in or equal to	$(q)$ the set of points $z$ satisfying $\operatorname{Im} z=0$
$(C)$ If $|\omega|=2$,then the set of points $z=\omega-1/\omega$ is contained in or equal to	$(r)$ the set of points $z$ satisfying $|\operatorname{Im} z| \leq 1$
$(D)$ If $|\omega|=1$,then the set of points $z=\omega+1/\omega$ is contained in or equal to	$(s)$ the set of points $z$ satisfying $|\operatorname{Re} z| \leq 1$
	$(t)$ the set of points $z$ satisfying $|z| \leq 3$

If $z = x + iy$ and the point $P$ in the Argand diagram represents $z$,then the locus of the point $P$ satisfying the equation $2|z - 2 - 3i| = 3|z - 2 + i|$ is a circle with centre