Let $z$ be the complex number with $\operatorname{Im}(z)=10$ and satisfying $\frac{2 \mathrm{z}-\mathrm{n}}{2 \mathrm{z}+\mathrm{n}}=2 \mathrm{i}-1$, where $\mathrm{i}=\sqrt{-1}$, for some natural number ' $n$ ' then

Argument of the complex number $z=\frac{13-5 i}{4-9 i}, i=\sqrt{-1}$ is

If $x=-2+\sqrt{-3}$, then the value of $2 x^4+5 x^3+7 x^2-x+38$ is equal to

$\mathrm{z}=\frac{3+2 \mathrm{i} \sin \theta}{1-2 \mathrm{i} \sin \theta},(\mathrm{i}=\sqrt{-1})$ will be purely imaginary if $\theta=$