[填空题]
Consider the polynomi3 )s z :yll(+;g2n 3fmsqlfjpwal r tdv:rumy/- kxc*n /62r w3pv$p(z)=z^{5}+z^{4}-z^{3}+z^{2}+4 z+2$ , for $z \in \mathbb{C}$ .
1. Write down the sum and product of the roots of p(z)=0 .sum of roots = product of roots =
2. Show that (z+1) is a factor of p(z) .
The polynomial can be written in the form $p(z)=(z+1)^{3}\left(z^{2}+c z+d\right)$ .
3. Find the value of c and the value of d .d = c =
4. Hence find the complex roots of p(z)=0 . $\pm \mathrm{i}$
