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

If $Z_1$ and $Z_2$ are complex numbers such that $|Z_1+Z_2|=|Z_1|+|Z_2|$,then the difference in the amplitudes of $Z_1$ and $Z_2$ is

Find the modulus and the argument of the complex number $z = -\sqrt{3} + i$.

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

If $z_1=(2,-1)$ and $z_2=(6,3)$,then $\operatorname{amp}\left(\frac{z_1-z_2}{z_1+z_2}\right)=$

If for complex numbers $z_1$ and $z_2$,$\arg(z_1/z_2) = 0$,then $|z_1 - z_2|$ is equal to