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 $\theta=$

If $\mathrm{z}=x+\mathrm{i} y$ is a complex number, then the equation $\left|\frac{z+i}{z-i}\right|=\sqrt{3}$ represents the