If $arg\,z < 0$ then $arg\,( - z) - arg\,(z)$ is equal to
$\pi $
$ - \pi $
$ - \frac{\pi }{2}$
$\frac{\pi }{2}$
Find the number of non-zero integral solutions of the equation $|1-i|^{x}=2^{x}$
If $z $ is a complex number of unit modulus and argument $\theta$, then ${\rm{arg}}\left( {\frac{{1 + z}}{{1 + (\bar z)}}} \right)$ equals.
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
The product of two complex numbers each of unit modulus is also a complex number, of
The modulus and amplitude of $\frac{{1 + 2i}}{{1 - {{(1 - i)}^2}}}$ are