$A$ point $z$ moves on the Argand diagram in such a way that $|z - 3i| = 2$. Then its locus will be:

The area of the triangle with vertices $A(z)$,$B(iz)$,and $C(z+iz)$ is

If $z = x + iy$ and the point $P$ represents $z$ in the Argand plane,then the locus of $z$ satisfying the equation $|z - 1| + |z + i| = 2$ is

If $z$ is a complex number such that $|z| \geq 1$,then the minimum value of $\left|z+\frac{1}{2}(3+4 i)\right|$ is:

Suppose that $z_{1}, z_{2}, z_{3}$ are three vertices of an equilateral triangle in the Argand plane. Let $\alpha = \frac{1}{2}(\sqrt{3} + i)$ and $\beta$ be a non-zero complex number. The points $\alpha z_{1} + \beta, \alpha z_{2} + \beta, \alpha z_{3} + \beta$ will be

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