If ${z_1}.{z_2}........{z_n} = z,$ then $arg\,{z_1} + arg\,{z_2} + ....$+$arg\,{z_n}$ and $arg$$z$ differ by a

If $|z_1| = 2 , |z_2| =3 , |z_3| = 4$ and $|2z_1 +3z_2 +4z_3| =9$ ,then value of $|8z_2z_3 +27z_3z_1 +64z_1z_2|$ is equal to:-

If $z$ is a complex number such that $|z - \bar{z}| = 2$ and $|z + \bar{z}| = 4 $, then which of the following is always incorrect -

Let $S=\left\{Z \in C: \bar{z}=i\left(z^2+\operatorname{Re}(\bar{z})\right)\right\}$. Then $\sum_{z \in S}|z|^2$ is equal to

The argument of the complex number $\frac{{13 - 5i}}{{4 - 9i}}$is

If $z = \cos \frac{\pi }{6} + i\sin \frac{\pi }{6}$ then