We define the values of $2$ complex numbers: $z_1=\sqrt[\phantom{2}]{3}+1j$ and $z_2=4-4j$ Without MATLAB$/$Python$/$calculator$,$ analytically compute expressions for:

a$)z_1{z}_1^{**}$

b$)\frac{z_1}{z_1+z_2}$

c$)j\frac{z_2}{z_1^2}$

d$)$ exp$(z_2)$

$(2$ pts each$)$