If $z = x + iy$ and $|z - zi| = 1,$ then

For any non-zero complex number $z$,the minimum value of $|z|+|z-1|$ is

Let $z=x+iy$ and a point $P$ represent $z$ in the Argand plane. If the real part of $\frac{z-1}{z+i}$ is $1$,then a point that lies on the locus of $P$ is

If the four complex numbers $z$,$\overline{z}$,$\overline{z}-2 \operatorname{Re}(\overline{z})$ and $z-2 \operatorname{Re}(z)$ represent the vertices of a square of side $4$ units in the Argand plane,then $|z|$ is equal to:

Let $z = x + iy$ be a complex number,$A = \{z : |z| \leq 2\}$ and $B = \{z : (1-i)z + (1+i)\bar{z} \geq 4\}$. Then which one of the following options belongs to $A \cap B$?

If a complex number $z=x+iy$ represents a point $P(x, y)$ in the Argand plane and $z$ satisfies the condition that the imaginary part of $\frac{z-3}{z+3i}$ is zero,then the locus of the point $P$ is