If the center and radius of the circle $\left|\frac{z-2}{z-3}\right|=2$ are respectively $(\alpha, \beta)$ and $\gamma$,then $3(\alpha+\beta+\gamma)$ is equal to

If $z_1, z_2, z_3$ are vertices of a triangle in the Argand plane such that $|z_1 - z_2| = |z_1 - z_3|$,then $\arg \left( \frac{2z_1 - z_2 - z_3}{z_3 - z_2} \right)$ is:

If $\operatorname{Re}\left(\frac{z-1}{2z+i}\right)=1,$ where $z=x+iy,$ then the point $(x, y)$ lies on a

If $\left| z - \frac{1 + 3i}{2} \right| = \frac{\sqrt{10}}{2}$ and $P$,$Q$,and $R$ are points representing the complex numbers $z$,$z e^{i \pi / 3}$,and $z(1 + e^{i \pi / 3})$ respectively in the Argand plane,then the area of the triangle $PQR$ is:

Let $z_{1}$ and $z_{2}$ be complex numbers such that $z_{1} \neq z_{2}$ and $|z_{1}|=|z_{2}|$. If $\operatorname{Re}(z_{1}) > 0$ and $\operatorname{Im}(z_{2}) < 0$, then $\frac{z_{1}+z_{2}}{z_{1}-z_{2}}$ is

The figure in the complex plane given by $10 z \bar{z} - 3(z^2 + \bar{z}^2) + 4i(z^2 - \bar{z}^2) = 0$ is