If $\bar z$ be the conjugate of the complex number $z$, then which of the following relations is false

Let $z_1, z_2 \in C$ such that $| z_1 + z_2 |= \sqrt 3$ and $|z_1| = |z_2| = 1,$ then the value of $|z_1 - z_2|$ is

If ${z_1}$ and ${z_2}$ are two complex numbers, then $|{z_1} - {z_2}|$ is

The sum of amplitude of $z$ and another complex number is $\pi $. The other complex number can be written

If $|z|\, = 4$ and $arg\,\,z = \frac{{5\pi }}{6},$then $z =$

Let $S=\left\{z \in C : z^{2}+\bar{z}=0\right\}$. Then $\sum \limits_{z \in S}(\operatorname{Re}(z)+\operatorname{Im}(z))$ is equal to$......$