Let $z$ be a complex number such that $\left|\frac{z-i}{z+2i}\right|=1$ and $|z|=\frac{5}{2}$. Then the value of $|z+3i|$ is:

Match the statements in column-$I$ with those in column-$II$.
[Note: Here $z$ takes the values in the complex plane and $\operatorname{Im} z$ and $\operatorname{Re} z$ denote,respectively,the imaginary part and the real part of $z$]

column-$I$	column-$II$
$(A)$ The set of points $z$ satisfying $|z-i|z||=|z+i|z||$ is contained in or equal to	$(p)$ an ellipse with eccentricity $\frac{4}{5}$
$(B)$ The set of points $z$ satisfying $|z+4|+|z-4|=10$ is contained in or equal to	$(q)$ the set of points $z$ satisfying $\operatorname{Im} z=0$
$(C)$ If $|\omega|=2$,then the set of points $z=\omega-1/\omega$ is contained in or equal to	$(r)$ the set of points $z$ satisfying $|\operatorname{Im} z| \leq 1$
$(D)$ If $|\omega|=1$,then the set of points $z=\omega+1/\omega$ is contained in or equal to	$(s)$ the set of points $z$ satisfying $|\operatorname{Re} z| \leq 1$
	$(t)$ the set of points $z$ satisfying $|z| \leq 3$

If the amplitude of $z-2-3i$ is $\frac{\pi}{4}$,then the locus of $z=x+iy$ is:

If ${z_1}, {z_2}, {z_3}, {z_4}$ are the affixes of four points in the Argand plane and $z$ is the affix of a point such that $|z - z_1| = |z - z_2| = |z - z_3| = |z - z_4|$,then ${z_1}, {z_2}, {z_3}, {z_4}$ are

The area of the triangle whose vertices are $i, \omega$ and $\omega^2$ is (Where $\omega$ is a complex cube root of unity other than $1$,$i$ is an imaginary number) . . . . . . sq.units

The point represented by $2 + i$ in the Argand plane moves $1 \, \text{unit}$ eastwards,then $2 \, \text{units}$ northwards and finally from there $2\sqrt{2} \, \text{units}$ in the south-westwards direction. Then its new position in the Argand plane is at the point represented by