If $z = \frac{(2-i)(1+i)^3}{(1-i)^2}$,then $\operatorname{Arg}(z) = $

$x$ 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 $x^6 y^4+\frac{1}{x^6 y^4}=$

Assertion $(A)$: If the arguments of $\bar{z}_1$ and $z_2$ are $\frac{\pi}{5}$ and $\frac{\pi}{3}$ respectively,then $\arg(z_1 z_2)$ is $\frac{2\pi}{15}$. Reason $(R)$: For any complex number $z$,$\arg(\bar{z}) = \frac{\pi}{2} + \arg(z)$. The correct option among the following is:

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

The amplitude (argument) of $(1+i)^{5}$ is

If ${z_1}, {z_2}$ and ${z_3}, {z_4}$ are two pairs of conjugate complex numbers,then $arg\left( \frac{z_1}{z_4} \right) + arg\left( \frac{z_2}{z_3} \right)$ equals: