If ${z_1}$ and ${z_2}$ are any two complex numbers then $|{z_1} + {z_2}{|^2}$ $ + |{z_1} - {z_2}{|^2}$ is equal to
$2|{z_1}{|^2}\,|{z_2}{|^2}$
$2|{z_1}{|^2} + \,2\,\,|{z_2}{|^2}$
$|{z_1}{|^2} + \,|{z_2}{|^2}$
$2|{z_1}|\,\,|{z_2}|$
The modulus and amplitude of $\frac{{1 + 2i}}{{1 - {{(1 - i)}^2}}}$ are
If a complex number $z$ statisfies the equation $x + \sqrt 2 \,\,\left| {z + 1} \right|\,+ \,i\, = \,0,$ then $\left| z \right|$ is equal to
For any two complex numbers ${z_1}$and${z_2}$ and any real numbers $a$ and $b$; $|(a{z_1} - b{z_2}){|^2} + |(b{z_1} + a{z_2}){|^2} = $
If ${z_1},{z_2} \in C$, then $amp\,\left( {\frac{{{{\rm{z}}_{\rm{1}}}}}{{{{{\rm{\bar z}}}_{\rm{2}}}}}} \right) = $
If $\frac{{z - i}}{{z + i}}(z \ne - i)$ is a purely imaginary number, then $z.\bar z$ is equal to