In the Argand plane,the vector $z = 4 - 3i$ is turned in the clockwise sense through $180^o$ and stretched three times. The complex number represented by the new vector is

If $z_1, z_2, z_3$ are the vertices of an equilateral triangle and $z$ is its circumcentre,then

$A$ man walks a distance of $3$ units from the origin towards the north-east $(N 45^{\circ} E)$ direction. From there,he walks a distance of $4$ units towards the north-west $(N 45^{\circ} W)$ direction to reach a point $P$. Then the position of $P$ in the Argand plane is

The points in the Argand plane represented by the complex conjugates of $1+2i, 2-3i, 3-4i$:

If $Z \neq \pm 1$ is a complex number and $\operatorname{Arg}\left(\frac{Z-1}{Z+1}\right)=\frac{\pi}{4}$,then the locus of $Z$ in the Argand plane is

The number of solutions of the equation $z^{2}+\overline{z}=0$,where $z \in \mathbb{C}$,is