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

The argument of the complex number $ - 1 + i\sqrt 3 $ is ............. $^\circ$

If $\alpha$ and $\beta$ are different complex numbers with $|\beta|=1,$ then find $\left|\frac{\beta-\alpha}{1-\bar{\alpha} \beta}\right|$

Let $z =1+ i$ and $z _1=\frac{1+ i \overline{ z }}{\overline{ z }(1- z )+\frac{1}{ z }}$. Then $\frac{12}{\pi}$ $\arg \left(z_1\right)$ is equal to $..........$.

If ${z_1},{z_2}$ are two complex numbers such that $\left| {\frac{{{z_1} - {z_2}}}{{{z_1} + {z_2}}}} \right| = 1$ and $i{z_1} = k{z_2}$, where $k \in R$, then the angle between ${z_1} - {z_2}$ and ${z_1} + {z_2}$ is

If $5 + ix^3y^2$ and $x^3 + y^2 + 6i$ are conjugate complex numbers and arg $(x + iy) = \theta $ , then ${\tan ^2}\,\theta $ is equal to