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:-

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

If $z_{1}=2-i, z_{2}=1+i,$ find $\left|\frac{z_{1}+z_{2}+1}{z_{1}-z_{2}+1}\right|$

If $z$ is a complex number, then the minimum value of $|z| + |z - 1|$ is

If $\alpha$ denotes the number of solutions of $|1-i|^x=2^x$ and $\beta=\left(\frac{|z|}{\arg (z)}\right)$, where $z=\frac{\pi}{4}(1+i)^4\left(\frac{1-\sqrt{\pi i}}{\sqrt{\pi}+i}+\frac{\sqrt{\pi}-i}{1+\sqrt{\pi} \mathrm{i}}\right), i=\sqrt{-1}$, then the distance of the point $(\alpha, \beta)$ from the line $4 x-3 y=7$ is

Let $a = lm\left( {\frac{{1 + {z^2}}}{{2iz}}} \right)$, where $z$ is any non-zero complex number. The set $A = \{ a:\left| z \right| = 1\,and\,z \ne  \pm 1\} $ is equal to