Question $3($DTFT and LTID system$)$

$($a$)$ If $x(e^j)$ is the DTFT of the sequence

$x[n]=\{1,2,3,4\},0n3$

Evaluate the values of following expressions:

i$)x(e^j)$;$(2^{\text{'}})$

ii$){\displaystyle \underset{-}{\overset{}{}}}x(e^j)d$; $(2\text{'})$

iii$){\displaystyle \underset{-}{\overset{}{}}}|x(e^j){|}^{2}d$; $(2\text{'})$

iv$){\displaystyle \underset{-}{\overset{}{}}}|\frac{dx(e^j)}{d}{|}^{2}d.(2^{\text{'}})$