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

The locus of the complex number $Z$ such that $\arg \left(\frac{Z-1}{Z+1}\right)=\frac{\pi}{4}$ is

In the Argand plane,the values of $z$ satisfying the equation $|z-1|=|i(z+1)|$ lie on

The locus of the points $z$ which satisfy the condition $\text{arg} \left( \frac{z - 1}{z + 1} \right) = \frac{\pi}{3}$ is

Let $A = \{z \in \mathbb{C} : |z - 2 - i| = 3\}$, $B = \{z \in \mathbb{C} : \operatorname{Re}(z - iz) = 2\}$ and $S = A \cap B$. Then $\sum_{z \in S} |z|^2$ is equal to . . . . . . .

If $z, iz$ and $z+iz$ are the vertices of a triangle and if $|z|=4$,then the area (in sq. units) of that triangle is: