If $z$ is a complex number of unit modulus and argument $\theta$, then $arg\left(\dfrac{1+z}{1+\overline{z}}\right)$ equals 

The modulus of the complex number $z$ such that $\left| z + 3 - i\right | = 1$ and $\arg{z} = \pi$ is equal to

Argument of the complex number  $\left( \dfrac { - 1 - 3 i } { 2 + i } \right).$

$z_{1}=-1-i \sqrt{3}, z_{2}=\sqrt{3}-i$.

If $x=9^{\frac {1}{3}} 9^{\frac {1}{9}} 9^{\frac {1}{27}} .....\infty, y=4^{\frac {1}{3}} 4^{\frac {-1}{9}} 4^{\frac {1}{27}}....\infty,$ and $z=\sum_{r=1}^{\infty} (1+i)^{-r}$, then $arg (x+yz)$ is equal to