Problem $1$: $[16$pts$]$ Prove the following properties of the CTFT$.$

Hint: Using the analysis and synthesis equations should be enough.

a$)[8$pts$]$ Parseval's identity:

${\displaystyle \underset{-}{\overset{}{}}}|x(t){|}^{2}dt=\frac{1}{2}{\displaystyle \underset{-}{\overset{}{}}}|x(j){|}^{2}d.$

b$)[8$pts$]$ Multiplication$-$convolution: if $)=(1,2,$ then $x_1(j)x_2(j)=F\{(x_1**x_2)(t)\}.$