If $z = \frac{{ - 2}}{{1 + \sqrt 3 \,i}}$ then the value of $arg\,(z)$ is

Let $a = lm\left( {\frac{{1 + {z^2}}}{{2iz}}} \right)$, where $z$ is any non-zero complex number. The set $A = \{ a:\left| z \right| = 1\,and\,z \ne  \pm 1\} $ is equal to

The conjugate of a complex number is $\frac{1}{{i - 1}}$ then that complex number is

Find the real numbers $x$ and $y$ if $(x-i y)(3+5 i)$ is the conjugate of $-6-24 i$

If complex numbers $z_1$, $z_2$ are such that $\left| {{z_1}} \right| = \sqrt 2 ,\left| {{z_2}} \right| = \sqrt 3$ and $\left| {{z_1} + {z_2}} \right| = \sqrt {5 - 2\sqrt 3 }$, then the value of $|Arg z_1 -Arg z_2|$ is

If a complex number $z$ statisfies the equation $x + \sqrt 2 \,\,\left| {z + 1} \right|\,+ \,i\, = \,0,$ then $\left| z \right|$ is equal to