$arg\,(5 - \sqrt 3 i) = $
${\tan ^{ - 1}}\frac{5}{{\sqrt 3 }}$
${\tan ^{ - 1}}\left( { - \,\frac{5}{{\sqrt 3 }}} \right)$
${\tan ^{ - 1}}\frac{{\sqrt 3 }}{5}$
${\tan ^{ - 1}}\left( { - \frac{{\sqrt 3 }}{5}} \right)$
If $z$ is a complex number satisfying $|z|^2 - |z| - 2 < 0$, then the value of $|z^2 + z sin \theta|$ , for all values of $\theta$ , is
Let $z$ be a complex number (not lying on $X$-axis) of maximum modulus such that $\left| {z + \frac{1}{z}} \right| = 1$. Then
Let $z_1$ and $z_2$ be two complex number such that $z_1$ $+z_2=5$ and $z_1^3+z_2^3=20+15 i$. Then $\left|z_1^4+z_2^4\right|$ equals-
Which of the following are correct for any two complex numbers ${z_1}$ and ${z_2}$
If $z = 1 - \cos \alpha + i\sin \alpha $, then $amp \ z$=