If complex numbers $(x -2y) + i(3x -y)$ and $(2x -y) + i(x -y + 6)$ are conjugates of each other, then $|x + iy|$ is $(x,y \in R)$ 
 

Let $\alpha$ and $\beta$ be the sum and the product of all the non-zero solutions of the equation $(\bar{z})^2+|z|=0, z \in C$. Then $4\left(\alpha^2+\beta^2\right)$ is equal to :

If ${z_1},{z_2},{z_3}$be three non-zero complex number, such that ${z_2} \ne {z_1},a = |{z_1}|,b = |{z_2}|$ and $c = |{z_3}|$ suppose that $\left| {\begin{array}{*{20}{c}}a&b&c\\b&c&a\\c&a&b\end{array}} \right| = 0$, then $arg\left( {\frac{{{z_3}}}{{{z_2}}}} \right)$ is equal to

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

If $z$ and $w$ are two complex numbers such that $|zw| = 1$ and $arg(z) -arg(w) =\frac {\pi }{2},$ then