If $\frac{z-1}{z+1}$ is purely imaginary, then

If the imaginary part of $\frac{2 z+1}{i z+1}$ is $-2$,then the locus of the point representing $z$ in the complex plane is

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

$S = \{z \in \mathbb{C} : |z + 1 - i| = 1\}$ represents

Let $z=x+iy$ be a complex number,where $x$ and $y$ are integers and $i=\sqrt{-1}$. Then the area of the rectangle whose vertices are the roots of the equation $z\bar{z}^3+\bar{z}z^3=350$ is

Let point $P = \alpha + i\beta$,where $\alpha, \beta > 0$,undergo the following three transformations successively on the Argand plane:
$(I)$ Reflection about $\text{amp}(z) = \frac{\pi}{4}$
$(II)$ Transformation through a distance $\beta$ units along the positive direction of the real axis
$(III)$ Rotation through an angle $\frac{\pi}{4}$ about the origin in the counter-clockwise direction
If the final position of the point is given by $Q = -\sqrt{2} + i\sqrt{6}$,then: