The argument of the complex number $\sin \,\frac{{6\pi }}{5}\, + \,i\,\left( {1\, + \,\cos \,\frac{{6\pi }}{5}} \right)$ is 

If ${z_1} = a + ib$ and ${z_2} = c + id$ are complex numbers such that $|{z_1}| = |{z_2}| = 1$ and $R({z_1}\overline {{z_2}} ) = 0,$ then the pair of complex numbers ${w_1} = a + ic$ and ${w_2} = b + id$ satisfies

The product of two complex numbers each of unit modulus is also a complex number, of

The amplitude of $\frac{{1 + \sqrt 3 \,i}}{{\sqrt 3 - i}}$ is

If $|{z_1}| = |{z_2}| = .......... = |{z_n}| = 1,$ then the value of $|{z_1} + {z_2} + {z_3} + ............. + {z_n}|$=

Let $\bar{z}$ denote the complex conjugate of a complex number $z$. If $z$ is a non-zero complex number for which both real and imaginary parts of

$(\bar{z})^2+\frac{1}{z^2}$

are integers, then which of the following is/are possible value($s$) of $|z|$ ?