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

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:

Let $O$ be the origin and $A$ be the point $z_{1} = 1 + 2i$. If $B$ is the point $z_{2}$ with $\operatorname{Re}(z_{2}) < 0$, such that $\triangle OAB$ is a right-angled isosceles triangle with $OB$ as the hypotenuse, then which of the following is $NOT$ true?

If $S = \{z \in \mathbb{C} : \frac{z-i}{z+2i} \in \mathbb{R}\}$,then:

Let $S = \{z = x + iy : \frac{2z - 3i}{4z + 2i} \text{ is a real number} \}$. Then which of the following is $NOT$ correct?

The value of $|z|^{2}+|z-3|^{2}+|z-i|^{2}$ is minimum when $z$ equals