PROBLEM $1\mathrm{.}1.*$ Simplify each of the following expressions and write the answer in both rectangular form and polar form. The first one is done for you. Summarize your answers in a table, like the one shown below, but also describe your approach and show your work in each case.

$($a$)z=j(1+j)$

POLAR

$($b$)z=\sqrt[\phantom{2}]{8}{e}^{j4\mathrm{.}5}(1+j)$

$($c$),z=(3-4j)(3+4j)$

$($d$)z=e^{j15}{e}^{-j\frac{}{3}}+e^{j12}{e}^{j\frac{}{3}}$

$($e$)z=\frac{1-j}{1+j}$

$\sqrt[\phantom{2}]{2}{e}^{j0\mathrm{.}75}$

$-1+j$

$\sqrt[\phantom{2}]{2}{e}^{j0\mathrm{.}75}$

$($b$)z=\sqrt[\phantom{2}]{8}{e}^{j4\mathrm{.}5}(1+j)$

$$

$($c$)z=(3-4j)(3+4j)$

$($d$)z=e^{j15}{e}^{-j\frac{}{3}}+e^{j12}{e}^{j\frac{}{3}}$

$$

$($f$)z=(1+j{)}^4-(1-j{)}^4$

$($g$),z=$jcos$(\frac{}{6})-sin(\frac{}{6})$

$q,$

$q,$