If $z$ is a complex number such that $|z| = 4$ and $\text{arg}(z) = \frac{5\pi}{6}$,then $z$ is equal to

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

Let $z$ be a complex number such that the principal value of argument, $\arg(z) > 0$. Then, $\arg(z) - \arg(-z)$ is

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