$|{z_1} + {z_2}| = |{z_1}| + |{z_2}|$ is possible if

If $z_1 = 10 + 6i$,$z_2 = 4 + 6i$ and $z$ is any complex number such that the argument of $\frac{z - z_1}{z - z_2}$ is $\frac{\pi}{4}$,then

Let $S_{1}=\{z_{1} \in \mathbb{C}:|z_{1}-3|=\frac{1}{2}\}$ and $S_{2}=\{z_{2} \in \mathbb{C}:|z_{2}-|z_{2}+1||=|z_{2}+|z_{2}-1||\}$. Then,for $z_{1} \in S_{1}$ and $z_{2} \in S_{2}$,the least value of $|z_{2}-z_{1}|$ is:

For $a, b, c, d \in R$, if $z_1 = a + ib$ and $z_2 = c + id$ are such that $|z_1| = |z_2| = 1$ and $\operatorname{Re}(z_1 \bar{z}_2) = 0$, then the pair of complex numbers $w_1 = a + ic$ and $w_2 = b + id$ satisfy

If $z=x+iy$ satisfies the condition $|z+1|=1$,then $z$ lies on the

If $\frac{z-1}{2z+1}$ is a purely imaginary number,then the locus of $z$ represents a circle. Find its radius.