If $i$ is the root of the equation $x^2+1=0$, then

$$ (1+\sqrt{3} i)^{2023}+(1-\sqrt{3} i)^{2023}= $$

One of the values of $(\sqrt{3}-i)^{\frac{1}{6}}$ is

If $a x^2-x y-3 y^2-5 x+20 y+c=0$ represents a pair of lines passing through the point $(2,3)$, then $a-c=$

$\operatorname{Arg}\left(\sin \frac{6 \pi}{5}+i\left(1+\cos \frac{6 \pi}{5}\right)\right)=$