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:-

Let $w$ $(Im\, w \neq 0)$ be a complex number. Then the set of all complex number $z$ satisfying the equation $w – \overline {w}z  = k\left( {1 – z} \right)$ , for some real number $k$, is

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

Let $z$ be a complex number. Then the angle between vectors $z$ and $ – iz$ is

If $\frac{3+i \sin \theta}{4-i \cos \theta}, \theta \in[0,2 \pi],$ is a real number, then an argument of $\sin \theta+\mathrm{i} \cos \theta$ is