If $z_1, z_2  $ are any two complex numbers, then $|{z_1} + \sqrt {z_1^2 - z_2^2} |$ $ + |{z_1} - \sqrt {z_1^2 - z_2^2} |$ is equal to

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

If ${z_1},{z_2} \in C$, then $amp\,\left( {\frac{{{{\rm{z}}_{\rm{1}}}}}{{{{{\rm{\bar z}}}_{\rm{2}}}}}} \right) = $

If ${Z_1} \ne 0$ and $Z_2$ be two complex numbers such that $\frac{{{Z_2}}}{{{Z_1}}}$ is a purely imaginary number, then $\left| {\frac{{2{Z_1} + 3{Z_2}}}{{2{Z_1} - 3{Z_2}}}} \right|$ is equal to 

Let $z$ and $w$ be the two non-zero complex numbers such that $|z|\, = \,|w|$ and $arg\,z + arg\,w = \pi $. Then $z$ is equal to

The amplitude of the complex number $z = \sin \alpha + i(1 - \cos \alpha )$ is