The locus of the point representing the complex number $z$ for which $|z+3|^2-|z-3|^2=15$ is

For all $z \in \mathbb{C}$ on the curve $C_1: |z| = 4$,let the locus of the point $w = z + \frac{1}{z}$ be the curve $C_2$. Then:

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

If $z = x + iy$ and the point $P$ represents $z$ in the Argand plane,then the locus of $z$ satisfying the equation $|z - 1| + |z + i| = 2$ 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

The vector $z = 3 - 4i$ is turned anticlockwise through an angle of $180^{\circ}$ and stretched $2.5$ times. The complex number corresponding to the newly obtained vector is