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 a complex number $z=x+iy$ represents a point $P$ on the Argand plane and $\operatorname{Arg}\left(\frac{z-(3-2i)}{z-(-2+3i)}\right)=\frac{\pi}{4}$,then the locus of $P$ is a

If $z_1$ and $z_2$ are two complex numbers satisfying the equation $\left|\frac{z_1+z_2}{z_1-z_2}\right|=1$,then $\frac{z_1}{z_2}$ may be

If $z = x + iy$,then the area of the triangle whose vertices are the points $z$,$iz$,and $z + iz$ is

For $a, b, c, d \in R$, if $z_1 = a + ib$ and $z_2 = c + id$ are such that $|z_1| = |z_2| = 1$ and $\operatorname{Re}(z_1 \bar{z}_2) = 0$, then the pair of complex numbers $w_1 = a + ic$ and $w_2 = b + id$ satisfy

The point $z$ in the Argand plane moves such that $\operatorname{Re} \left( \frac{iz + 1}{iz - 1} \right) = 2$. Then the locus of $z$ is: