Number of complex numbers $z$ such that $\left| z \right| + z - 3\bar z = 0$ is equal to

Argument and modulus of $\frac{{1 + i}}{{1 - i}}$ are respectively

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$......$

If $z = x + iy$ satisfies $|z|-2=0$ and $|z-i|-|z+5 i|=0$, then

The solutions of equation in $z$, $| z |^2 -(z + \bar{z}) + i(z - \bar{z})$ + $2$ = $0$ are $(i = \sqrt{-1})$

For any complex number $z,\bar z = \left( {\frac{1}{z}} \right)$if and only if