$\left| {(1 + i)\frac{{(2 + i)}}{{(3 + i)}}} \right| = $
$ - \frac{1}{2}$
$\frac{1}{2}$
$1$
$ - 1$
If ${z_1}$ and ${z_2}$ are two non-zero complex numbers such that $|{z_1} + {z_2}| = |{z_1}| + |{z_2}|,$then arg $({z_1}) - $arg $({z_2})$ is equal to
A real value of $x$ will satisfy the equation $\left( {\frac{{3 - 4ix}}{{3 + 4ix}}} \right) = $ $\alpha - i\beta \,(\alpha ,\beta \,{\rm{real),}}$ if
The argument of the complex number $\sin \,\frac{{6\pi }}{5}\, + \,i\,\left( {1\, + \,\cos \,\frac{{6\pi }}{5}} \right)$ is
If $\alpha$ and $\beta$ are different complex numbers with $|\beta|=1,$ then find $\left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right|$
If $z$ is a purely real number such that ${\mathop{\rm Re}\nolimits} (z) < 0$, then $arg(z)$ is equal to