If $z$ is a complex number,then the curves $|z|=1$,$|z-2|=1$,and $|z-1|=0$ have a common point at

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

If $z$ is a complex number such that $|z| \ge 2$,then the minimum value of $|z + \frac{1}{2}|$ is:

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:

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

Let $C$ be the circle in the complex plane with centre $z_0 = \frac{1}{2}(1 + 3i)$ and radius $r = 1$. Let $z_1 = 1 + i$ and the complex number $z_2$ be outside the circle $C$ such that $|z_1 - z_0| |z_2 - z_0| = 1$. If $z_0, z_1$ and $z_2$ are collinear,then the smaller value of $|z_2|^2$ is equal to $.............$.