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

$x$ and $y$ are two complex numbers such that $|x|=|y|=1$. If $\operatorname{Arg}(x)=2 \alpha$,$\operatorname{Arg}(y)=3 \beta$,and $\alpha+\beta=\frac{\pi}{36}$,then $x^6 y^4+\frac{1}{x^6 y^4}=$

The sum of the argument of $z$ and another complex number is $\pi$. The other complex number can be written as:

If $z=1+i \sqrt{3}$ then $|\operatorname{Arg} z|+|\operatorname{Arg} \bar{z}|$ is equal to

If ${z_1}$ and ${z_2}$ are two non-zero complex numbers such that $|{z_1} + {z_2}| = |{z_1}| + |{z_2}|,$ then $\text{arg}({z_1}) - \text{arg}({z_2})$ is equal to

If $Arg(z)$ denotes the principal argument of a complex number $z$,then the value of the expression $Arg\left( -i e^{i\frac{\pi}{9}} z^2 \right) + 2Arg\left( 2i e^{-i\frac{\pi}{18}} \bar{z} \right)$ is