If $z$ is a complex number,then the minimum value of $|z| + |z - 1|$ is

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 $z \neq 1$ and $\frac{z^2}{z-1}$ is real,then the point represented by the complex number $z$ lies:

If ${z_1}$ and ${z_2}$ are complex numbers such that ${z_1} \neq {z_2}$ and $|{z_1}| = |{z_2}|$. If ${z_1}$ has a positive real part and ${z_2}$ has a negative imaginary part,then $\frac{{z_1 + z_2}}{{z_1 - z_2}}$ may be

If $z = x + iy$ and $\omega = \frac{1 - iz}{z - i}$,then $|\omega| = 1$ shows that in the complex plane:

If $S = \{z \in \mathbb{C} : |z - i| = |z + i| = |z - 1|\}$,then $n(S)$ is: