Without explicitly determining the time$-$limited sequence x$[$k$]$ for the following DFT:

X$[$r$]=[12,8+$j$4,5,4+$j$1,16,16,4$j$1,5,8$j$4],$X$[$r$]=[12,\backslash$; $8+$ j$4,\backslash$; $-5,\backslash$; $4+$ j$1,\backslash$; $16,\backslash$; $16,\backslash$; $4-$ j$1,\backslash$; $-5,\backslash$; $8-$ j$4],$X$[$r$]=[12,8+$j$4,5,4+$j$1,16,16,4$j$1,5,8$j$4],$

compute the following functions of the DFT X$[$r$]$:

$($i$)$ x$[0]$;

$($ii$)$ x$[9]$

$($iii$)$k$=08$x$[$k$]\backslash$sum$\_\{$k$=0\}^\{8\}$ x$[$k$]$

$($iv$)$k$=08$x$[$k$]2\backslash$sum$\_\{$k$=0\}^\{8\}|$x$[$k$]|^2$