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

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

The locus of $z$ given by $\left| \frac{z - 1}{z - i} \right| = 1$ is

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

In the complex plane,let $z_1=\sqrt{3}+i$ and $z_2=\sqrt{3}-i$ be two adjacent vertices of an $n$-sided regular polygon centered at the origin. Then,$n$ equals

If $a$ is a complex number and $b$ is a real number,then the equation $\bar{a}+a+b=0$ represents $a$ as a: